tag:blogger.com,1999:blog-20384599763345601002024-02-19T18:53:10.403+07:00MGMP Matematika SMK Kab BoyolaliTingkatkan Kualitas Guru Matematika SMK BoyolaliMGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.comBlogger113125tag:blogger.com,1999:blog-2038459976334560100.post-41902920485874622532020-04-21T05:09:00.001+07:002020-04-25T11:17:45.914+07:00SOAL ULANGAN KENAIKAN KELAS SMK tahun 2019-2020 dan kunci jawabBerikut kami berikan latihan soal Ulangan Kenaikan Kelas (UKK)<br />
atau latihan Soal Penialaian Akhir Tahun (PAT) tahun lalu disertai kunci jawab<br />
semoga bisa digunakan unruk mencoba dan latihan di rumah masing-masing<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaAK33trJMDvYoH_TBmRtYB5ZXXLlmPRCrg587NsyR_TXNMbAoUTJdTMVBRlDW0zLNa1mtOGB3i317KdQIfojrLlTMIQctptEDfNQES25tynpfPfRh7ekRVmnsGZR2c8cdicvz46P2_YH8/s1600/soal+kls+x.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="429" data-original-width="651" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaAK33trJMDvYoH_TBmRtYB5ZXXLlmPRCrg587NsyR_TXNMbAoUTJdTMVBRlDW0zLNa1mtOGB3i317KdQIfojrLlTMIQctptEDfNQES25tynpfPfRh7ekRVmnsGZR2c8cdicvz46P2_YH8/s320/soal+kls+x.jpg" width="320" /></a></div>
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<div style="text-align: center;">
Soal kelas x download <a href="http://raboninco.com/MlUq" target="_blank">disini</a></div>
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Download <a href="http://raboninco.com/KPMm" target="_blank">Kunci jawab kelas x</a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0HPR1qKFN63Edp8xA-MFHzQmJtWIAYvM-A_T1SM74b5AeWF6KjawFHoeIsqXPw2D-XS6Urug5SYC6V2q09Jr9A0evC71XUMZF50JYOppomNeex064AFIqc1FQIMf8IxxhzqpxZGG0Krdp/s1600/soal+kls+xi.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="568" data-original-width="727" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0HPR1qKFN63Edp8xA-MFHzQmJtWIAYvM-A_T1SM74b5AeWF6KjawFHoeIsqXPw2D-XS6Urug5SYC6V2q09Jr9A0evC71XUMZF50JYOppomNeex064AFIqc1FQIMf8IxxhzqpxZGG0Krdp/s320/soal+kls+xi.jpg" width="320" /></a></div>
<div style="text-align: center;">
soal kelas xi download <a href="http://raboninco.com/KQHt" target="_blank">disini</a></div>
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download <a href="http://raboninco.com/KQJf" target="_blank">Kunci Jabab kelas xi</a></div>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-70071740330121720872020-04-20T17:21:00.000+07:002020-04-20T17:23:06.294+07:00Kisi kisi PAT (Penilaian Akhir Tahun) Matematika SMK tahun 2019/2020Sebentar lagi akan dilaksanakan Penilaian Akhir Tahun (PAT ) atau Ulangan Kenaikan Kelas (UKK)<br />
<br />
dibawah kami sampaikan Kisi-kisi atau indikator soal PAT untuk siswa SMK kelas X dan XI<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit8BjhKjiVqFuL3r6x0Kb1BC7xqRfEmKqQsCMgUGRCZD1277TJJ5-ZUZipSQAWpLwAdOy3-lmIhLBzmNWwwUJsym3UkYRpcIyvd6u2YR3q9qnDErtJLaDV__tohFUeCf2Jw_-ajIE5egM/s1600/kisi+x.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="428" data-original-width="611" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit8BjhKjiVqFuL3r6x0Kb1BC7xqRfEmKqQsCMgUGRCZD1277TJJ5-ZUZipSQAWpLwAdOy3-lmIhLBzmNWwwUJsym3UkYRpcIyvd6u2YR3q9qnDErtJLaDV__tohFUeCf2Jw_-ajIE5egM/s320/kisi+x.jpg" width="320" /></a></div>
<br />
download Kisi-Kisi kelas X <a href="http://raboninco.com/K3wL" target="_blank">disini</a><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDEixVP1MhyphenhyphenXGRgdXI-5F-pQxYsoEfbvaVILb279ythTgWEVy-OiFJxMq76DaEBcJIC20z_C27KtYjpSpbNYdNBY8ow-4Pfh7kvMPqNSJ8PwtGHIB93Q8YVBVaZvliXeU0bTaxe0nVx94/s1600/kisi+xi.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="676" height="189" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDEixVP1MhyphenhyphenXGRgdXI-5F-pQxYsoEfbvaVILb279ythTgWEVy-OiFJxMq76DaEBcJIC20z_C27KtYjpSpbNYdNBY8ow-4Pfh7kvMPqNSJ8PwtGHIB93Q8YVBVaZvliXeU0bTaxe0nVx94/s320/kisi+xi.jpg" width="320" /></a></div>
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dan Kisi-kisi kelas XI <a href="http://raboninco.com/K44p" target="_blank">disini</a>MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-36963259586228797692019-11-01T22:15:00.000+07:002019-11-03T16:44:11.634+07:00Kisi - kisi PAS Gasal 2019-2020Semester gasal mendekati akhir, saatnya mempersipakn soal PAS gasal, silahkan download kisi-kisi PAS gasal berikut ini<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdLe3fOZOKY1Yz9gGsho6C-2ulBu-ndlaq4p6hlXHgqsMJ4z1I0gyZ1A0pE-iTLdIZg0i396SUaZrMS9YO_ds2Q6sUAFOC9gihR6jxdv3LRolQj3NILHGr-5fC91PcT42yvdqOh7DOTUI/s1600/kisi-kisi.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="173" data-original-width="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdLe3fOZOKY1Yz9gGsho6C-2ulBu-ndlaq4p6hlXHgqsMJ4z1I0gyZ1A0pE-iTLdIZg0i396SUaZrMS9YO_ds2Q6sUAFOC9gihR6jxdv3LRolQj3NILHGr-5fC91PcT42yvdqOh7DOTUI/s1600/kisi-kisi.jpg" /></a><br />
<a href="http://bit.ly/kisi-x-1920" target="_blank">Kelas x kurikulum 2013</a><br />
<br />
<a href="http://bit.ly/2PFkKOX" target="_blank">Kelas XI Kurikulum 2013</a><br />
<br />
<a href="http://bit.ly/kisi-xii-1920" target="_blank">Kelas XII Kurikulum K-13 </a><br />
<br />
Semoga bermanfaatMGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com1tag:blogger.com,1999:blog-2038459976334560100.post-26404243188636448262019-09-13T10:48:00.000+07:002019-09-13T10:48:14.563+07:00Limit Fungsi<h2 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 23px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Pengertian Limit Fungsi</h2>
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Limit merupakan sebuah konsep <span style="color: blue; font-family: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; word-break: normal;">matematika</span> dimana sesuatu dikatakan “hampir” atau “mendekati” nilai suatu bilangan tertentu. Limit dapat berupa sebuah fungsi yang kodomainnya “hampir” atau “mendekati” nilai suatu bilangan asli tertentu.</div>
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Limit Fungsi Aljabar</h2>
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Dalam pengoperasian limit fungsi aljabar, terdapat beberapa hukum atau teorema limit yang perlu diperhatikan. Jika k konstanta, <span style="color: blue; font-family: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; word-break: normal;">fungsi</span> f dan fungsi g adalah fungsi-fungsi memiliki nilai limit yang mendekati bilangan c, maka:</div>
<table style="background-color: #f9f9f9; border-collapse: collapse; border-spacing: 0px; border: 0px; color: black; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; width: auto; word-break: normal;"><tbody style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">No</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331">TEOREMA</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">1</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}k=k" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7Dk%3Dk&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}k=k" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">2</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}x = c" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7Dx+%3D+c&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}x = c" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">3</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="k \cdot \lim \limits_{x\to c}f(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=k+%5Ccdot+%5Clim+%5Climits_%7Bx%5Cto+c%7Df%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="k \cdot \lim \limits_{x\to c}f(x)" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">4</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x \to c}({f(x) + g(x)})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx+%5Cto+c%7D%28%7Bf%28x%29+%2B+g%28x%29%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x \to c}({f(x) + g(x)})" /> <img alt="= \lim_{x\to c}f(x) + \lim_{x\to c}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim_%7Bx%5Cto+c%7Df%28x%29+%2B+%5Clim_%7Bx%5Cto+c%7Dg%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim_{x\to c}f(x) + \lim_{x\to c}g(x)" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">5</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_x\to c({f(x) - g(x)}) = \lim_x\to c{f(x) - g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_x%5Cto+c%28%7Bf%28x%29+-+g%28x%29%7D%29+%3D+%5Clim_x%5Cto+c%7Bf%28x%29+-+g%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_x\to c({f(x) - g(x)}) = \lim_x\to c{f(x) - g(x)}" /> <img alt="= \lim_x{\to c}f(x) - \lim_{x \to c}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim_x%7B%5Cto+c%7Df%28x%29+-+%5Clim_%7Bx+%5Cto+c%7Dg%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim_x{\to c}f(x) - \lim_{x \to c}g(x)" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">6</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}({f(x) \cdot g(x)}) = \lim_{x\to c}f(x) \cdot \lim_{x\to c}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7D%28%7Bf%28x%29+%5Ccdot+g%28x%29%7D%29+%3D+%5Clim_%7Bx%5Cto+c%7Df%28x%29+%5Ccdot+%5Clim_%7Bx%5Cto+c%7Dg%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}({f(x) \cdot g(x)}) = \lim_{x\to c}f(x) \cdot \lim_{x\to c}g(x)" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">7</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"> <img alt="\lim \limits_{x\to c}\frac{f(x)}{g(x)} = \frac{\lim_{x\to c}f(x)}{\lim_{x\to c}g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D+%3D+%5Cfrac%7B%5Clim_%7Bx%5Cto+c%7Df%28x%29%7D%7B%5Clim_%7Bx%5Cto+c%7Dg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}\frac{f(x)}{g(x)} = \frac{\lim_{x\to c}f(x)}{\lim_{x\to c}g(x)}" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">8</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}(f(x)^n) = (\lim_{x\to c}f(x))^n" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7D%28f%28x%29%5En%29+%3D+%28%5Clim_%7Bx%5Cto+c%7Df%28x%29%29%5En&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}(f(x)^n) = (\lim_{x\to c}f(x))^n" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">9</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}(\sqrt[n]{f(x)}) = \sqrt[n]{\lim_{x\to c}f(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7D%28%5Csqrt%5Bn%5D%7Bf%28x%29%7D%29+%3D+%5Csqrt%5Bn%5D%7B%5Clim_%7Bx%5Cto+c%7Df%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}(\sqrt[n]{f(x)}) = \sqrt[n]{\lim_{x\to c}f(x)}" /></td></tr>
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Ada tiga metode dalam mengerjakan limit fungsi aljabar, yaitu:</div>
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1. Metode substitusi</h3>
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Metode paling mudah dengan menentukan hasil suatu limit fungsi adalah dengan mensubstitusi langsung nilai kedalam fungsi f(x). Syarat metode ini adalah jika hasil substitusi tidak membentuk nilai “tak tentu”. Contoh:</div>
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<img alt="\lim \limits_{x\to 3}\frac{x^2 - 4}{x + 2} = \frac{9 - 4}{3 + 2} = 1" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+3%7D%5Cfrac%7Bx%5E2+-+4%7D%7Bx+%2B+2%7D+%3D+%5Cfrac%7B9+-+4%7D%7B3+%2B+2%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 3}\frac{x^2 - 4}{x + 2} = \frac{9 - 4}{3 + 2} = 1" /></div>
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2. Metode pemfaktoran</h3>
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Jika pada metode substitusi menghasilkan suatu nilai bentuk tak tentu seperti:</div>
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∞, <img alt="\frac{0}{0}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B0%7D%7B0%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\frac{0}{0}" />, <img alt="\frac{\infty}{\infty}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B%5Cinfty%7D%7B%5Cinfty%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\frac{\infty}{\infty}" />, 0 x∞, ∞ – ∞, 0<span style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">0</span>, ∞<span style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">0</span>, atau ∞<span style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">∞</span></div>
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maka fungsi tersebut harus difaktorkan terlebih dahulu sehingga bentuknya tidak menjadi bentuk tak tentu, baru kemudian bisa disubstitusikan <img alt="x\to c" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=x%5Cto+c&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="x\to c" />. Contoh:</div>
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<img alt="\lim \limits_{x\to 3}\frac{x^2 - 3x}{2x - 6} = \frac{x(x - 3)}{2(x - 3)} = \frac{3}{2}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+3%7D%5Cfrac%7Bx%5E2+-+3x%7D%7B2x+-+6%7D+%3D+%5Cfrac%7Bx%28x+-+3%29%7D%7B2%28x+-+3%29%7D+%3D+%5Cfrac%7B3%7D%7B2%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 3}\frac{x^2 - 3x}{2x - 6} = \frac{x(x - 3)}{2(x - 3)} = \frac{3}{2}" /></div>
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3. Metode perkalian dengan akar sekawan</h3>
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Metode ini digunakan jika pada metode substitusi langsung menghasilkan nilai limit yang irasional. Fungsi dikalikan dengan akar sekawannya agar bentuk limit tersebut tidak irasional, sehingga bisa dilakukan kembali substitusi langsung nilai <img alt="x\to c" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=x%5Cto+c&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="x\to c" />. Contoh:</div>
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<img alt="\lim \limits_{x\to -1}\frac{x +1}{1 - \sqrt{x + 2}} x (\frac{1 + \sqrt{x +2}}{1 + \sqrt{x + 2}}) = \frac{(x + 1)(1 + \sqrt{x+ 2})}{1 - (x + 2)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+-1%7D%5Cfrac%7Bx+%2B1%7D%7B1+-+%5Csqrt%7Bx+%2B+2%7D%7D+x+%28%5Cfrac%7B1+%2B+%5Csqrt%7Bx+%2B2%7D%7D%7B1+%2B+%5Csqrt%7Bx+%2B+2%7D%7D%29+%3D+%5Cfrac%7B%28x+%2B+1%29%281+%2B+%5Csqrt%7Bx%2B+2%7D%29%7D%7B1+-+%28x+%2B+2%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to -1}\frac{x +1}{1 - \sqrt{x + 2}} x (\frac{1 + \sqrt{x +2}}{1 + \sqrt{x + 2}}) = \frac{(x + 1)(1 + \sqrt{x+ 2})}{1 - (x + 2)}" /></div>
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<img alt="=\frac{(x + 1)(1+\sqrt{x+2})}{-x - 1} = \frac{(x+1)(1+\sqrt{x+2})}{-(x+1)} = -(1 + \sqrt{x + 2})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D%5Cfrac%7B%28x+%2B+1%29%281%2B%5Csqrt%7Bx%2B2%7D%29%7D%7B-x+-+1%7D+%3D+%5Cfrac%7B%28x%2B1%29%281%2B%5Csqrt%7Bx%2B2%7D%29%7D%7B-%28x%2B1%29%7D+%3D+-%281+%2B+%5Csqrt%7Bx+%2B+2%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=\frac{(x + 1)(1+\sqrt{x+2})}{-x - 1} = \frac{(x+1)(1+\sqrt{x+2})}{-(x+1)} = -(1 + \sqrt{x + 2})" /></div>
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<img alt="=-(1 + \sqrt{-(1) + 2}) = -(1 + 1) = -2" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D-%281+%2B+%5Csqrt%7B-%281%29+%2B+2%7D%29+%3D+-%281+%2B+1%29+%3D+-2&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=-(1 + \sqrt{-(1) + 2}) = -(1 + 1) = -2" /></div>
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Dalam pengoprasian limit fungsi aljabar, terkadang nilai x mendekati <span style="color: blue; font-family: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; word-break: normal;">tak berhingga</span> (∞), sehingga jika disubstitusikan fungsi menghasilkan nilai tak tentu. Dalam pengoperasian limitnya, terdapat beberapa hukum atau teorema limit yang perlu diperhatikan. Jika n adalah bilangan bulat, k konstanta, fungsi f dan fungsi g adalah fungsi-fungsi memiliki nilai limit yang mendekati bilangan c, maka:</div>
<table style="background-color: #f9f9f9; border-collapse: collapse; border-spacing: 0px; border: 0px; color: black; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; width: auto; word-break: normal;"><tbody style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">No</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331">TEOREMA</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156">SYARAT</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">1</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}k = k" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dk+%3D+k&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}k = k" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156">k adalah konstanta</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td rowspan="2" style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">2</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}x^n = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dx%5En+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}x^n = \infty" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}\frac{1}{x^n} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7B1%7D%7Bx%5En%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{1}{x^n} = 0" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td rowspan="2" style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">3</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to -\infty}\frac{1}{x^n} = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+-%5Cinfty%7D%5Cfrac%7B1%7D%7Bx%5En%7D+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to -\infty}\frac{1}{x^n} = \infty" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156">Jika n = genap</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to - \infty}\frac{1}{x^n}= - \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+-+%5Cinfty%7D%5Cfrac%7B1%7D%7Bx%5En%7D%3D+-+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to - \infty}\frac{1}{x^n}= - \infty" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156">Jika n = ganjil</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">4</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}k \cdot f(x) = k \cdot \lim \limits_{x\to \infty}f(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dk+%5Ccdot+f%28x%29+%3D+k+%5Ccdot+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}k \cdot f(x) = k \cdot \lim \limits_{x\to \infty}f(x)" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156">k adalah konstanta</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">5</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}({f(x) + g(x)}) = \lim \limits_{x\to \infty} f(x) + \lim \limits_{x\to \infty}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%7Bf%28x%29+%2B+g%28x%29%7D%29+%3D+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D+f%28x%29+%2B+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}({f(x) + g(x)}) = \lim \limits_{x\to \infty} f(x) + \lim \limits_{x\to \infty}g(x)" /> <img alt="\lim \limits_{x\to \infty}{f(x) + g(x)} = \lim \limits_{x\to \infty} f(x) + \lim \limits_{x\to \infty}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%7Bf%28x%29+%2B+g%28x%29%7D+%3D+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D+f%28x%29+%2B+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}{f(x) + g(x)} = \lim \limits_{x\to \infty} f(x) + \lim \limits_{x\to \infty}g(x)" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">6</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}({f(x) - g(x)})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%7Bf%28x%29+-+g%28x%29%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}({f(x) - g(x)})" /> <img alt="= \lim \limits_{x\to \infty}f(x) - \lim \limits_{x\to \infty}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29+-+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to \infty}f(x) - \lim \limits_{x\to \infty}g(x)" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">7</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}({f(x) \cdot g(x)}) = \lim \limits_{x\to \infty}f(x) \cdot \lim \limits_{x\to \infty} g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%7Bf%28x%29+%5Ccdot+g%28x%29%7D%29+%3D+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29+%5Ccdot+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D+g%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}({f(x) \cdot g(x)}) = \lim \limits_{x\to \infty}f(x) \cdot \lim \limits_{x\to \infty} g(x)" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">8</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}\frac{f(x)}{g(x)} = \frac{\lim \limits_{x\to \infty}f(x)}{\lim \limits_{x\to \infty}g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D+%3D+%5Cfrac%7B%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29%7D%7B%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{f(x)}{g(x)} = \frac{\lim \limits_{x\to \infty}f(x)}{\lim \limits_{x\to \infty}g(x)}" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">9</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}(f(x)^n) = (\lim \limits_{x\to c} f(x))^n" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=+%5Clim+%5Climits_%7Bx%5Cto+c%7D%28f%28x%29%5En%29+%3D+%28%5Clim+%5Climits_%7Bx%5Cto+c%7D+f%28x%29%29%5En&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}(f(x)^n) = (\lim \limits_{x\to c} f(x))^n" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">10</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to c}(\sqrt[n]{f(x)}) = \sqrt[n]{\lim \limits_{x\to c}f(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+c%7D%28%5Csqrt%5Bn%5D%7Bf%28x%29%7D%29+%3D+%5Csqrt%5Bn%5D%7B%5Clim+%5Climits_%7Bx%5Cto+c%7Df%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to c}(\sqrt[n]{f(x)}) = \sqrt[n]{\lim \limits_{x\to c}f(x)}" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td rowspan="2" style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="34">11</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"> <img alt="\lim \limits_{x\to \infty}\frac{1}{f(x)} = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7B1%7D%7Bf%28x%29%7D+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{1}{f(x)} = \infty" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"><img alt="\lim \limits_{x\to \infty}f(x) = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}f(x) = 0" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="331"><img alt="\lim \limits_{x\to \infty}\frac{1}{f(x)} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7B1%7D%7Bf%28x%29%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{1}{f(x)} = 0" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="156"><img alt="\lim \limits_{x\to \infty}f(x) = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}f(x) = \infty" /></td></tr>
</tbody></table>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<br /></div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Ada dua metode dalam mengerjakan limit fungsi aljabar bentuk tak berhingga:</div>
<ol style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; list-style-image: initial; list-style-position: outside; margin: 0px 0px 20px 30px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">Membagi dengan pangkat tertinggi</li>
</ol>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Metode ini digunakan pada limit fungsi bentuk <img alt="\lim \limits_{x\to \infty}\frac{f(x)}{g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{f(x)}{g(x)}" />. Metode ini dapat dikerjakan dengan membagi pembilang f(x) dan penyebut g(x) dengan variabel x<span style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">n</span> berpangkat tertinggi yang ada dalam fungsi f(x) dan g(x). Setelahnya, baru dapat disubstitusi dengan <img alt="x\to \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=x%5Cto+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="x\to \infty" />. Contoh:</div>
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<img alt="\lim \limits_{x\to \infty}\frac{4x-1}{x^2+2} = \frac{\frac{4x}{x^2} - \frac{1}{x^2}}{\frac{x^2}{x^2} + \frac{2}{x^2}} = \frac{\frac{4}{x} - \frac{1}{x^2}}{1+\frac{2}{x^2}} = \frac{0}{1} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7B4x-1%7D%7Bx%5E2%2B2%7D+%3D+%5Cfrac%7B%5Cfrac%7B4x%7D%7Bx%5E2%7D+-+%5Cfrac%7B1%7D%7Bx%5E2%7D%7D%7B%5Cfrac%7Bx%5E2%7D%7Bx%5E2%7D+%2B+%5Cfrac%7B2%7D%7Bx%5E2%7D%7D+%3D+%5Cfrac%7B%5Cfrac%7B4%7D%7Bx%7D+-+%5Cfrac%7B1%7D%7Bx%5E2%7D%7D%7B1%2B%5Cfrac%7B2%7D%7Bx%5E2%7D%7D+%3D+%5Cfrac%7B0%7D%7B1%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}\frac{4x-1}{x^2+2} = \frac{\frac{4x}{x^2} - \frac{1}{x^2}}{\frac{x^2}{x^2} + \frac{2}{x^2}} = \frac{\frac{4}{x} - \frac{1}{x^2}}{1+\frac{2}{x^2}} = \frac{0}{1} = 0" /></div>
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<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">Mengalikan bentuk sekawan</li>
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Metode ini digunakan pada limit fungsi bentuk <img alt="\lim \limits_{x\to \infty}f(x) - \lim \limits_{x\to \infty}g(x)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29+-+%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}f(x) - \lim \limits_{x\to \infty}g(x)" />. Metode ini dapat diselesaikan dengan perkalian bentuk sekawan:</div>
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<img alt="\frac{\lim \limits_{x\to \infty}f(x)+\lim \limits_{x\to \infty}g(x)}{\lim \limits_{x\to \infty}f(x)+\lim \limits_{x \to \infty}g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29%2B%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Dg%28x%29%7D%7B%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7Df%28x%29%2B%5Clim+%5Climits_%7Bx+%5Cto+%5Cinfty%7Dg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\frac{\lim \limits_{x\to \infty}f(x)+\lim \limits_{x\to \infty}g(x)}{\lim \limits_{x\to \infty}f(x)+\lim \limits_{x \to \infty}g(x)}" /></div>
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kemudian dilanjutkan pembagian dengan metode pertama yaitu membagi dengan pangkat tertinggi. Contoh:</div>
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<img alt="\lim \limits_{x\to \infty}(\sqrt{x^2 + 4x - 5 - \sqrt{x^2 -x -2}})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%5Csqrt%7Bx%5E2+%2B+4x+-+5+-+%5Csqrt%7Bx%5E2+-x+-2%7D%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}(\sqrt{x^2 + 4x - 5 - \sqrt{x^2 -x -2}})" /></div>
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<img alt="=\lim \limits_{n\to \infty}(\sqrt{x^2 + 4x -5 - \sqrt{x^2 - x - 2}})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D%5Clim+%5Climits_%7Bn%5Cto+%5Cinfty%7D%28%5Csqrt%7Bx%5E2+%2B+4x+-5+-+%5Csqrt%7Bx%5E2+-+x+-+2%7D%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=\lim \limits_{n\to \infty}(\sqrt{x^2 + 4x -5 - \sqrt{x^2 - x - 2}})" /> <img alt="x \frac{(\sqrt{x^2+4x-5 + \sqrt{x^2 - x - 2}})}{(\sqrt{x^2+4x-5} + \sqrt{x^2-x-2})}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=x+%5Cfrac%7B%28%5Csqrt%7Bx%5E2%2B4x-5+%2B+%5Csqrt%7Bx%5E2+-+x+-+2%7D%7D%29%7D%7B%28%5Csqrt%7Bx%5E2%2B4x-5%7D+%2B+%5Csqrt%7Bx%5E2-x-2%7D%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="x \frac{(\sqrt{x^2+4x-5 + \sqrt{x^2 - x - 2}})}{(\sqrt{x^2+4x-5} + \sqrt{x^2-x-2})}" /></div>
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<img alt="= \lim \limits_{n\to \infty}\frac{((x^2+4x-5) - (x^2-x-2))}{(\sqrt{x^2+4x-5} + \sqrt{x^2-x-2})}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bn%5Cto+%5Cinfty%7D%5Cfrac%7B%28%28x%5E2%2B4x-5%29+-+%28x%5E2-x-2%29%29%7D%7B%28%5Csqrt%7Bx%5E2%2B4x-5%7D+%2B+%5Csqrt%7Bx%5E2-x-2%7D%29%7D+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{n\to \infty}\frac{((x^2+4x-5) - (x^2-x-2))}{(\sqrt{x^2+4x-5} + \sqrt{x^2-x-2})}" /> <img alt="= \lim \limits_{n\to \infty}frac{5x-3}{(\sqrt{x^2+4x-5})+\sqrt{x^2-x-2}}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bn%5Cto+%5Cinfty%7Dfrac%7B5x-3%7D%7B%28%5Csqrt%7Bx%5E2%2B4x-5%7D%29%2B%5Csqrt%7Bx%5E2-x-2%7D%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{n\to \infty}frac{5x-3}{(\sqrt{x^2+4x-5})+\sqrt{x^2-x-2}}" /></div>
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Kemudian pembilang dan penyebut dibagi x pangkat tertinggi yaitu x<span style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">1</span>:</div>
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<img alt="\lim \limits_{n\to \infty}\frac{\frac{5x}{x}-\frac{3}{x}}{(\sqrt{\frac{x^2+4x-5}{x^2}}+\sqrt{\frac{x^2-x-2}{x^2}})}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bn%5Cto+%5Cinfty%7D%5Cfrac%7B%5Cfrac%7B5x%7D%7Bx%7D-%5Cfrac%7B3%7D%7Bx%7D%7D%7B%28%5Csqrt%7B%5Cfrac%7Bx%5E2%2B4x-5%7D%7Bx%5E2%7D%7D%2B%5Csqrt%7B%5Cfrac%7Bx%5E2-x-2%7D%7Bx%5E2%7D%7D%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{n\to \infty}\frac{\frac{5x}{x}-\frac{3}{x}}{(\sqrt{\frac{x^2+4x-5}{x^2}}+\sqrt{\frac{x^2-x-2}{x^2}})}" /> <img alt="= \lim \limits_{n\to \infty}\frac{5-\frac{3}{x}}{(\sqrt{1+\frac{4}{x}-\frac{5}{x^2}}+ \sqrt{1-\frac{1}{x}-\frac{2}{x^2}})}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bn%5Cto+%5Cinfty%7D%5Cfrac%7B5-%5Cfrac%7B3%7D%7Bx%7D%7D%7B%28%5Csqrt%7B1%2B%5Cfrac%7B4%7D%7Bx%7D-%5Cfrac%7B5%7D%7Bx%5E2%7D%7D%2B+%5Csqrt%7B1-%5Cfrac%7B1%7D%7Bx%7D-%5Cfrac%7B2%7D%7Bx%5E2%7D%7D%29%7D+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{n\to \infty}\frac{5-\frac{3}{x}}{(\sqrt{1+\frac{4}{x}-\frac{5}{x^2}}+ \sqrt{1-\frac{1}{x}-\frac{2}{x^2}})}" /></div>
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<img alt="= \frac{(-0}{(1+1)} = \frac{5}{2}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Cfrac%7B%28-0%7D%7B%281%2B1%29%7D+%3D+%5Cfrac%7B5%7D%7B2%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \frac{(-0}{(1+1)} = \frac{5}{2}" /></div>
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Limit Fungsi Trigonometri</h2>
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Limit juga dapat digunakan pada fungsi <span style="color: blue; font-family: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; word-break: normal;">trigonometri</span>. Penyelesaiannya sama dengan fungsi limit aljabar. Namun, agar mengerti penjalasan selanjutnya harus mengerti terlebih dahulu konsep dari trigonometri. Penyelesaian dalam limit fungsi ini dalam trigonometri bisa dilakukan dengan melakukan perubahan-perubahan bentuk sinus, cosinus, dan tangen.</div>
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Ada tiga bentuk umum dalam limit fungsi trigonometri, yaitu bentuk :</div>
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1. Bentuk <img alt="\lim_{x\to c}f(x) = f(c)" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim_%7Bx%5Cto+c%7Df%28x%29+%3D+f%28c%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim_{x\to c}f(x) = f(c)" /></h3>
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Pada bentuk ini, limit dari fungsi trigonometri f(x) merupakan hasil dari substitusi nilai c ke dalam x dari trigonometri. Contoh :</div>
<table style="background-color: #f9f9f9; border-collapse: collapse; border-spacing: 0px; border: 0px; color: black; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; width: auto; word-break: normal;"><tbody style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="49">No.</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="126">CONTOH</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="132">NILAI LIMIT</td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="49">1</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="126"><img alt="\lim \limits_{x\to ^\pi/_4} \sin 2x" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5E%5Cpi%2F_4%7D+%5Csin+2x&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to ^\pi/_4} \sin 2x" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="132"> <img alt="\sin \frac{\pi}{2}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Csin+%5Cfrac%7B%5Cpi%7D%7B2%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\sin \frac{\pi}{2}" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="49">2</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="126"><img alt="\lim \limits_{x\to \pi} \cos \frac{1}{2}x" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cpi%7D+%5Ccos+%5Cfrac%7B1%7D%7B2%7Dx&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \pi} \cos \frac{1}{2}x" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="132"><img alt="cos\frac{1}{2}\pi" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=cos%5Cfrac%7B1%7D%7B2%7D%5Cpi&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="cos\frac{1}{2}\pi" /></td></tr>
<tr style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="49">3</td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="126"><img alt="\lim \limits_{x\to ^\pi/_2} \tan x" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5E%5Cpi%2F_2%7D+%5Ctan+x&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to ^\pi/_2} \tan x" /></td><td style="border-collapse: collapse; border: 1px solid rgb(0, 0, 0); font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;" width="132"> <img alt="\tan\frac{\pi}{2}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Ctan%5Cfrac%7B%5Cpi%7D%7B2%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\tan\frac{\pi}{2}" /></td></tr>
</tbody></table>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Jika c = 0, maka rumus limit-limit trigonometrinya adalah sebagai berikut :</div>
<ul style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; list-style: outside square; margin: 0px 0px 20px 30px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0} \sin x = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D+%5Csin+x+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0} \sin x = 0" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0} \cos x = 1" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D+%5Ccos+x+%3D+1&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0} \cos x = 1" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0} \cos x = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D+%5Ccos+x+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0} \cos x = 0" /></li>
</ul>
<h3 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 18px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
2. Bentuk <img alt="\lim_{x\to c}\frac{f(x)}{g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim_%7Bx%5Cto+c%7D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim_{x\to c}\frac{f(x)}{g(x)}" /></h3>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Pada bentuk ini, limit diperoleh dari perbandingan 2 trigonometri berbeda. Kedua trigonometri tersebut jika langsung disubstitusi dengan nilai c menghasilkan f(c) = 0 dan g(c) = 0. Sehingga, nilai limit trigonometri tersebut menjadi bilangan tak tentu<img alt="\frac{0}{0}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B0%7D%7B0%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\frac{0}{0}" />. Penyelesaiannya sama dengan limit fungsi aljabar yaitu pemfaktoran. Contoh bentuk ini yaitu:</div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="\lim \limits_{x\to ^\pi/_2}\frac{\sin 2x}{cosx} = \frac{2 \cos x \sin x}{cosx} = 2 \sin x = 2 \sin \frac{\pi}{2} = 2" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5E%5Cpi%2F_2%7D%5Cfrac%7B%5Csin+2x%7D%7Bcosx%7D+%3D+%5Cfrac%7B2+%5Ccos+x+%5Csin+x%7D%7Bcosx%7D+%3D+2+%5Csin+x+%3D+2+%5Csin+%5Cfrac%7B%5Cpi%7D%7B2%7D+%3D+2&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to ^\pi/_2}\frac{\sin 2x}{cosx} = \frac{2 \cos x \sin x}{cosx} = 2 \sin x = 2 \sin \frac{\pi}{2} = 2" /></div>
<h3 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 18px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
3. Bentuk <img alt="\lim_{x\to 0}\frac{f(x)}{g(x)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim_%7Bx%5Cto+0%7D%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim_{x\to 0}\frac{f(x)}{g(x)}" /></h3>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Pada bentuk ini, limit diperoleh dari perbandingan antara trigonometri dan fungsi aljabar. Jika disubstitusikan langsung akan menghaslikan bilangan tak tentu. Pada bentuk ini dikerjakan dengan konsep <span style="color: blue; font-family: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; word-break: normal;">turunan</span>. Bentuk rumus dasar limit ini adalah:</div>
<ul style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; list-style: outside square; margin: 0px 0px 20px 30px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\sin x}{x} = \lim_{x\to 0}\frac{x}{\sin x} = 1" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Csin+x%7D%7Bx%7D+%3D+%5Clim_%7Bx%5Cto+0%7D%5Cfrac%7Bx%7D%7B%5Csin+x%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\sin x}{x} = \lim_{x\to 0}\frac{x}{\sin x} = 1" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{x}{\cos x} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7Bx%7D%7B%5Ccos+x%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{x}{\cos x} = 0" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\cos x}{x} = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Ccos+x%7D%7Bx%7D+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\cos x}{x} = \infty" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\tan x}{x} = \lim_{x\to}\frac{x}{\tan x} = 1" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Ctan+x%7D%7Bx%7D+%3D+%5Clim_%7Bx%5Cto%7D%5Cfrac%7Bx%7D%7B%5Ctan+x%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\tan x}{x} = \lim_{x\to}\frac{x}{\tan x} = 1" /></li>
</ul>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Berdasarkan rumus dasar diataas, jika dikembangkan menjadi rumus-rumus berikut:</div>
<div class="code-block code-block-6" style="background-color: #f9f9f9; border: 0px; clear: both; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin: 8px auto; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
</div>
<ul style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; list-style: outside square; margin: 0px 0px 20px 30px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\sin ax}{bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Csin+ax%7D%7Bbx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\sin ax}{bx} = \frac{a}{b}" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{ax}{\sin bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7Bax%7D%7B%5Csin+bx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{ax}{\sin bx} = \frac{a}{b}" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{ax}{\cos bx} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7Bax%7D%7B%5Ccos+bx%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{ax}{\cos bx} = 0" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\cos ax}{bx} = \infty" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Ccos+ax%7D%7Bbx%7D+%3D+%5Cinfty&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\cos ax}{bx} = \infty" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\tan ax}{bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Ctan+ax%7D%7Bbx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\tan ax}{bx} = \frac{a}{b}" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{ax}{\tan bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7Bax%7D%7B%5Ctan+bx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{ax}{\tan bx} = \frac{a}{b}" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\sin ax}{\tan bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Csin+ax%7D%7B%5Ctan+bx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\sin ax}{\tan bx} = \frac{a}{b}" /></li>
<li style="border: 0px; font: inherit; margin: 0px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;"><img alt="\lim \limits_{x\to 0}\frac{\tan ax}{\sin bx} = \frac{a}{b}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%5Cfrac%7B%5Ctan+ax%7D%7B%5Csin+bx%7D+%3D+%5Cfrac%7Ba%7D%7Bb%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}\frac{\tan ax}{\sin bx} = \frac{a}{b}" /></li>
</ul>
<h2 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 23px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Contoh Soal Limit Fungsi dan Pembahasan</h2>
<h3 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 18px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Contoh Soal Limit 1</h3>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Tentukanlah nilai dari <img alt="\lim_{x\to 2}(\frac{6-x}{x^2-4} - \frac{1}{x-2})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim_%7Bx%5Cto+2%7D%28%5Cfrac%7B6-x%7D%7Bx%5E2-4%7D+-+%5Cfrac%7B1%7D%7Bx-2%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim_{x\to 2}(\frac{6-x}{x^2-4} - \frac{1}{x-2})" /> (UAN 2002)</div>
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Pembahasan 1 :</div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="\lim \limits_{x\to 2}(\frac{6-x}{x^2} - \frac{1}{x-2}) = \lim \limits_{x\to 2}(\frac{6-x}{x^2-4} - \frac{x+2}{(x-2)(x+2)})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+2%7D%28%5Cfrac%7B6-x%7D%7Bx%5E2%7D+-+%5Cfrac%7B1%7D%7Bx-2%7D%29+%3D+%5Clim+%5Climits_%7Bx%5Cto+2%7D%28%5Cfrac%7B6-x%7D%7Bx%5E2-4%7D+-+%5Cfrac%7Bx%2B2%7D%7B%28x-2%29%28x%2B2%29%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 2}(\frac{6-x}{x^2} - \frac{1}{x-2}) = \lim \limits_{x\to 2}(\frac{6-x}{x^2-4} - \frac{x+2}{(x-2)(x+2)})" /> <img alt="= \lim \limits_{x\to 2}\frac{(6-x) - (x+2)}{(x-2)(x+2)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+2%7D%5Cfrac%7B%286-x%29+-+%28x%2B2%29%7D%7B%28x-2%29%28x%2B2%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to 2}\frac{(6-x) - (x+2)}{(x-2)(x+2)}" /></div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="=\lim \limits_{x\to 2}\frac{4-2x}{(x-2)(x+2)} = \lim \limits_{x\to 2}\frac{-2(x-2)}{(x-2)(x+2)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D%5Clim+%5Climits_%7Bx%5Cto+2%7D%5Cfrac%7B4-2x%7D%7B%28x-2%29%28x%2B2%29%7D+%3D+%5Clim+%5Climits_%7Bx%5Cto+2%7D%5Cfrac%7B-2%28x-2%29%7D%7B%28x-2%29%28x%2B2%29%7D+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=\lim \limits_{x\to 2}\frac{4-2x}{(x-2)(x+2)} = \lim \limits_{x\to 2}\frac{-2(x-2)}{(x-2)(x+2)}" /> <img alt="= \lim \limits_{x\to 2}\frac{-2}{(x+2)}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+2%7D%5Cfrac%7B-2%7D%7B%28x%2B2%29%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to 2}\frac{-2}{(x+2)}" /></div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="=-\frac{2}{4} = -\frac{1}{2}" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D-%5Cfrac%7B2%7D%7B4%7D+%3D+-%5Cfrac%7B1%7D%7B2%7D&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=-\frac{2}{4} = -\frac{1}{2}" /></div>
<h3 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 18px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Contoh Soal Limit 2</h3>
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Tentukanlah nilai dari <img alt="\lim \limits_{x\to \infty}(\frac{\sqrt{4x+x^2} - \sqrt{2+x^2}}{3x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%5Cfrac%7B%5Csqrt%7B4x%2Bx%5E2%7D+-+%5Csqrt%7B2%2Bx%5E2%7D%7D%7B3x%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}(\frac{\sqrt{4x+x^2} - \sqrt{2+x^2}}{3x})" /> (UN 2009)</div>
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Pembahasan 2:</div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="\lim \limits_{x\to \infty}(\frac{\sqrt{4x+x^2}-\sqrt{2+x^2}}{3x}) = \lim_{x\to \infty}(\frac{\sqrt{\frac{4}{x^2}+\frac{x^2}{x^2}}-\sqrt{\frac{2}{x^2}+\frac{x^2}{x^2}}}{\frac{3x}{x}})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+%5Cinfty%7D%28%5Cfrac%7B%5Csqrt%7B4x%2Bx%5E2%7D-%5Csqrt%7B2%2Bx%5E2%7D%7D%7B3x%7D%29+%3D+%5Clim_%7Bx%5Cto+%5Cinfty%7D%28%5Cfrac%7B%5Csqrt%7B%5Cfrac%7B4%7D%7Bx%5E2%7D%2B%5Cfrac%7Bx%5E2%7D%7Bx%5E2%7D%7D-%5Csqrt%7B%5Cfrac%7B2%7D%7Bx%5E2%7D%2B%5Cfrac%7Bx%5E2%7D%7Bx%5E2%7D%7D%7D%7B%5Cfrac%7B3x%7D%7Bx%7D%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to \infty}(\frac{\sqrt{4x+x^2}-\sqrt{2+x^2}}{3x}) = \lim_{x\to \infty}(\frac{\sqrt{\frac{4}{x^2}+\frac{x^2}{x^2}}-\sqrt{\frac{2}{x^2}+\frac{x^2}{x^2}}}{\frac{3x}{x}})" /> <img alt="= \lim_{x\to \infty}(\frac{\sqrt{\frac{4}{x^2}+1}-\sqrt{\frac{2}{x^2}+1}}{3})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim_%7Bx%5Cto+%5Cinfty%7D%28%5Cfrac%7B%5Csqrt%7B%5Cfrac%7B4%7D%7Bx%5E2%7D%2B1%7D-%5Csqrt%7B%5Cfrac%7B2%7D%7Bx%5E2%7D%2B1%7D%7D%7B3%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim_{x\to \infty}(\frac{\sqrt{\frac{4}{x^2}+1}-\sqrt{\frac{2}{x^2}+1}}{3})" /></div>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; text-align: center; vertical-align: baseline; word-break: normal;">
<img alt="=(\frac{1-1}{3}) = \frac{0}{3} = 0" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D%28%5Cfrac%7B1-1%7D%7B3%7D%29+%3D+%5Cfrac%7B0%7D%7B3%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=(\frac{1-1}{3}) = \frac{0}{3} = 0" /></div>
<h3 style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 18px; font-weight: normal; line-height: 1.6; margin: 0px 0px 10px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Contoh Soal Limit 3</h3>
<div style="background-color: #f9f9f9; border: 0px; font-family: arial, Arial, Helvetica, sans-serif; font-size: 15px; line-height: inherit; margin-bottom: 20px; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: baseline; word-break: normal;">
Tentukanlah nilai dari <img alt="\lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{1- \cos 2x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%2B+%5Csin+x+%5Ctan+x%7D%7B1-+%5Ccos+2x%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{1- \cos 2x})" /> (SPMB 2002)</div>
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Pembahasan 3 :</div>
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<img alt="\lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{1- \cos 2x}) = \lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{2sin^2x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%2B+%5Csin+x+%5Ctan+x%7D%7B1-+%5Ccos+2x%7D%29+%3D+%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%2B+%5Csin+x+%5Ctan+x%7D%7B2sin%5E2x%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="\lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{1- \cos 2x}) = \lim \limits_{x\to 0}(\frac{x^2+ \sin x \tan x}{2sin^2x})" /> <img alt="= \lim \limits_{x\to 0}(\frac{x^2}{2 \sin^2x}+\frac{\sin x \tan x}{2sin^2x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%7D%7B2+%5Csin%5E2x%7D%2B%5Cfrac%7B%5Csin+x+%5Ctan+x%7D%7B2sin%5E2x%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to 0}(\frac{x^2}{2 \sin^2x}+\frac{\sin x \tan x}{2sin^2x})" /></div>
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<img alt="= \lim \limits_{x\to 0}(\frac{x^2}{2sin^2x}+\frac{\sin x \tan x}{2 \sin^2x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%7D%7B2sin%5E2x%7D%2B%5Cfrac%7B%5Csin+x+%5Ctan+x%7D%7B2+%5Csin%5E2x%7D%29+&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to 0}(\frac{x^2}{2sin^2x}+\frac{\sin x \tan x}{2 \sin^2x})" /> <img alt="= \lim \limits_{x\to 0}(\frac{x^2}{2 \sin^2x}+\frac{\tan x}{2 \sin x})" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bx%5Cto+0%7D%28%5Cfrac%7Bx%5E2%7D%7B2+%5Csin%5E2x%7D%2B%5Cfrac%7B%5Ctan+x%7D%7B2+%5Csin+x%7D%29&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="= \lim \limits_{x\to 0}(\frac{x^2}{2 \sin^2x}+\frac{\tan x}{2 \sin x})" /></div>
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<img alt="=(\frac{1}{2(1^2)}+\frac{1}{2(1)}) = \frac{1}{2}+\frac{1}{2} = 1" class="latex jetpack-lazy-image jetpack-lazy-image--handled" src="https://s0.wp.com/latex.php?latex=%3D%28%5Cfrac%7B1%7D%7B2%281%5E2%29%7D%2B%5Cfrac%7B1%7D%7B2%281%29%7D%29+%3D+%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" style="border: 0px; font: inherit; height: auto; margin: 0px; max-width: 100%; outline: 0px; overflow-wrap: normal; padding: 0px; vertical-align: middle; word-break: normal;" title="=(\frac{1}{2(1^2)}+\frac{1}{2(1)}) = \frac{1}{2}+\frac{1}{2} = 1" /></div>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-79144529285557477792018-05-16T07:44:00.000+07:002019-10-03T19:52:56.371+07:00Kalender Pendidikan Tahun 2018 - 2019 Prop Jateng<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKQ5hyphenhyphenxHNu2fnXNcokkFzc07RQ1Wqgw0VuZnn-tx2T1fxficq0KWUPVx2BOQu6jgG8B0JIzu64fn1wWzNKI3OWCqTx0ujnEXUJjyuG6ecky5TGfIA0UFWUwREEk2Jd8LRnF8U7UwrwhO8/s1600/kaldik.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="444" data-original-width="840" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKQ5hyphenhyphenxHNu2fnXNcokkFzc07RQ1Wqgw0VuZnn-tx2T1fxficq0KWUPVx2BOQu6jgG8B0JIzu64fn1wWzNKI3OWCqTx0ujnEXUJjyuG6ecky5TGfIA0UFWUwREEk2Jd8LRnF8U7UwrwhO8/s320/kaldik.jpg" width="320" /></a></div>
<br />
silahkan downoad file nya <a href="http://zipansion.com/g4Z8" target="_blank">disini</a><br />
<br />
untuk yg membutuhkan modul - modul matematika SMA - SMK <a href="https://mgmp-mat-smk-byl.blogspot.com/2019/09/modul-pembelajaran-matematika-sma-dan.html" target="_blank">klik disini</a>MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com1tag:blogger.com,1999:blog-2038459976334560100.post-76363673038256823162018-05-16T07:24:00.001+07:002019-11-07T19:18:14.035+07:00Kisi - kisi Penlaian Akhir Tahun / Ulangan kenaikan Kelas 2017-2018Kisi - kisi Penlaian Akhir Tahun / Ulangan kenaikan Kelas<br />
Matematika SMK<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShxWedoBGd5J0PBwFpOBdEWljnrHqR-AvzrQjUJWdDDcwyI965EsQC-tcwJ5C8fPMcCy2dIZCLxIe3NtOQKffHU3H-HAkAcFPo_90M49MqJ_0oeZib4c_y7blYg2ct11fTrKZwLS_F4Kq/s1600/images.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="137" data-original-width="368" height="119" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShxWedoBGd5J0PBwFpOBdEWljnrHqR-AvzrQjUJWdDDcwyI965EsQC-tcwJ5C8fPMcCy2dIZCLxIe3NtOQKffHU3H-HAkAcFPo_90M49MqJ_0oeZib4c_y7blYg2ct11fTrKZwLS_F4Kq/s320/images.png" width="320" /></a></div>
<br />
silahkan di download kisi-kisi soal penilaian Akhir Tahun / Ulangan Kenaikan kelas<br />
<br />
ada dua kurikulum yang berlaku untuk kelas XI yakni KTSP dan K-13<br />
sedangkan untuk kelas X menggunakan kurikulum K-13 semua program keahlian<br />
<br />
1. Kelas X (<a href="http://zipansion.com/g3dX" target="_blank">K-13 semua jurusan</a> )<br />
<br />
2. kelas XI - <a href="http://zipansion.com/g3fj" target="_blank">K 13</a><br />
- <a href="http://zipansion.com/g3jD" target="_blank">Teknik (KTSP)</a><br />
- <a href="http://zipansion.com/g3kL" target="_blank">Non teknik (KTSP)</a><br />
<br />
<br />
Kisi-kisi PAS Gasal 2019-2020 <a href="https://mgmp-mat-smk-byl.blogspot.com/2019/11/kisi-kisi-pas-gasal-2019-2020.html" target="_blank">disini</a><br />
<br />MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-22935305759640900902018-01-25T22:50:00.000+07:002018-01-25T23:02:27.655+07:00POS UN Tahun Pelajaran 2017/2018 dan Surat Edaran tentang Revisi POS UN TP 2017/2018<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtUxtDCGR0QGdKFb9b1M15C_z_Uxa-Lp1JMF0kKY3GUlU2XYsN-kjv57rjN59nNb_9wjJgVw3vHGe5wu-7Qz4kabBK9aG_ytjz9zqXn_MX-mpogDqLgxypqHRII71zpKZe1dTPRFzNm1A/s1600/pos+un.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="163" data-original-width="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtUxtDCGR0QGdKFb9b1M15C_z_Uxa-Lp1JMF0kKY3GUlU2XYsN-kjv57rjN59nNb_9wjJgVw3vHGe5wu-7Qz4kabBK9aG_ytjz9zqXn_MX-mpogDqLgxypqHRII71zpKZe1dTPRFzNm1A/s1600/pos+un.png" /></a></div>
<div>
<span style="color: #666666; font-family: titillium, arial, sans-serif;"><span style="font-size: 18px;"><br /></span></span></div>
<div>
<span style="color: #666666; font-family: titillium, arial, sans-serif;"><span style="font-size: 18px;"><br /></span></span></div>
<ol style="background-color: white; border: 0px; color: #666666; font-family: Titillium, Arial, sans-serif; font-size: 18px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: inherit; list-style: none; margin: 0px 0px 15px 30px; padding: 0px; vertical-align: baseline;">
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Prosedur Operasional Standar (POS) Penyelenggaraan Ujian Nasional Tahun Pelajaran 2017/2018 (<a href="http://swiftation.com/877z" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Surat Edaran BSNP Nomor; 0088/SDAR/BSNP/I/2018 tentang <span lang="IN" style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Revisi POS </span>UN <span lang="IN" style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Tahun Pelajaran 201</span>7<span lang="IN" style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">/</span>2018<span style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span> (<a href="http://swiftation.com/87BB" target="_blank">unduh disini</a>);</li>
</ol>
MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-40439971899712214072018-01-25T22:48:00.000+07:002019-10-03T04:50:23.926+07:00Kisi-Kisi Ujian Sekolah Berstandar Nasional Tahun Pelajaran 2017/2018<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0YFfBWTrsV0m72SaMXzP4YnXraX0MKINMH3Kbpdg7VD04zeLepUxKnvPrAxx_KgYWwJt3hyphenhyphenUTCUHmSNwpqourx9Yfmhd4GTAjMPyKHlDuN7j4DFCvzKb2ulHjZexYR4P6GofcFqJUJX4/s1600/kisi+kisi.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="196" data-original-width="257" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0YFfBWTrsV0m72SaMXzP4YnXraX0MKINMH3Kbpdg7VD04zeLepUxKnvPrAxx_KgYWwJt3hyphenhyphenUTCUHmSNwpqourx9Yfmhd4GTAjMPyKHlDuN7j4DFCvzKb2ulHjZexYR4P6GofcFqJUJX4/s1600/kisi+kisi.png" /></a></div>
<h1 class="post-title entry-title" style="background-color: white; border: 0px; color: #444444; font-family: Titillium, Arial, sans-serif; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; font-weight: 400; letter-spacing: -1px; line-height: 1.5em; margin: 0px 0px 10px; padding: 0px; vertical-align: baseline; word-wrap: break-word;">
<span style="font-size: large;"><br /></span></h1>
<h1 class="post-title entry-title" style="background-color: white; border: 0px; color: #444444; font-family: Titillium, Arial, sans-serif; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; font-weight: 400; letter-spacing: -1px; line-height: 1.5em; margin: 0px 0px 10px; padding: 0px; vertical-align: baseline; word-wrap: break-word;">
<span style="font-size: large;">Berikut disampaikan Kisi-Kisi Ujian Sekolah Berstandar Nasional Tahun Pelajaran 2017/2018</span></h1>
<div class="entry themeform" style="background-color: white; border: 0px; color: #666666; font-family: Titillium, Arial, sans-serif; font-size: 1.125em; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.6em; margin: 0px; padding: 0px; vertical-align: baseline;">
<div class="entry-inner" style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">
<ol style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: none; margin: 0px 0px 15px 30px; padding: 0px; vertical-align: baseline;">
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SD/MI sederajat (<a href="http://swiftation.com/86kZ" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SMP/MTs sederajat (<a href="http://swiftation.com/86nt" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SMA/MA sederajat (<a href="http://swiftation.com/86pn" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SMK/MAK (<a href="http://swiftation.com/86sF" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SDLB/MILB (<a href="http://swiftation.com/86uS" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN SMPLB/MTsLB (<a href="http://swiftation.com/86x8" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN dan SMALB/MALB (<a href="http://swiftation.com/870D" target="_blank">unduh disini</a>)</li>
<li style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style: decimal; margin: 0px; padding: 0px; vertical-align: baseline;">Kisi-kisi USBN Pendidikan Kesetaraan (<a href="http://swiftation.com/874D" target="_blank">unduh disini</a>)</li>
</ol>
<div>
<a href="https://mgmp-mat-smk-byl.blogspot.com/2019/09/modul-pembelajaran-matematika-sma-dan.html" target="_blank">Kumpulan modul SMA/SMK</a></div>
</div>
</div>
MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-45994183766992154492018-01-25T22:05:00.001+07:002018-01-25T22:08:52.358+07:00Soal Olympiade SMA Kabupaten 2017<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3rTVtYX6r9dbpzwnM4Gy4IZ5TX120RiZMQW2XgAD2X2pEj_FkjOaHIdqMUMQDcQmuOZ6IFQeqg1Wbw7DuMvGsZtLeeXk2bKBy4AaYkFIkwfLCmzOkhTrNu6dmbPo3xQM1GkhNiJtglhc/s1600/download.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="241" data-original-width="209" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3rTVtYX6r9dbpzwnM4Gy4IZ5TX120RiZMQW2XgAD2X2pEj_FkjOaHIdqMUMQDcQmuOZ6IFQeqg1Wbw7DuMvGsZtLeeXk2bKBy4AaYkFIkwfLCmzOkhTrNu6dmbPo3xQM1GkhNiJtglhc/s1600/download.png" /></a></div>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
<br /></h3>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
MATEMATIKA</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Matematika 2017 [<a href="http://swiftation.com/802z" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Matematika 2017 [<a href="http://swiftation.com/806V" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
FISIKA</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Fisika 2017 [<a href="http://swiftation.com/809N" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Fisika 2017 [<a href="http://swiftation.com/817x" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
KIMIA</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Kimia 2017 [<a href="http://swiftation.com/81EM" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Kimia 2017 [<a href="http://swiftation.com/81JI" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
BIOLOGI</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Biologi 2017 [<a href="http://swiftation.com/81Pk" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Biologi 2017 [<a href="http://swiftation.com/81UI" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
KOMPUTER</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Komputer 2017 [<a href="http://swiftation.com/81eM" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Komputer 2017 [<a href="http://swiftation.com/81k6" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
ASTRONOMI</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Astronomi 2017 [<a href="http://swiftation.com/81nG" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Astronomi 2017 [<a href="http://swiftation.com/81rf" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
EKONOMI</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Ekonomi 2017 [<a href="http://swiftation.com/81up" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Ekonomi 2017 [D<a href="http://swiftation.com/81wv" target="_blank">ownload Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
KEBUMIAN</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Kebumian 2017 [<a href="http://swiftation.com/820k" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Kebumian 2017 [<a href="http://swiftation.com/823m" target="_blank">Download Kunci</a>]</blockquote>
<h3 style="background-color: white; color: #333333; font-family: Roboto, Arial, sans-serif; font-size: 20px; line-height: 1.2em; margin: 10px 0px; padding: 0px; width: 738.984px;">
GEOGRAFI</h3>
<blockquote style="background: rgb(252, 250, 248); border-left: 4px solid rgb(72, 232, 0); color: #444444; font-family: Georgia, serif; font-size: 18px; margin: 0px; padding-left: 8px;">
A. Soal OSK Geografi 2017 [<a href="http://swiftation.com/826k" target="_blank">Download Soal</a>]<br />
B. Kunci Jawaban OSK Geografi 2017 [<a href="http://swiftation.com/829B" target="_blank">Download Kunci</a>]</blockquote>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh64CCkj8xxpZdNEBKPZUFfzZ69viR9K4g-wCoHlgxqumUcAACWOi1pgEts9EYdKO8JFm9MJ6GmRAPoOtxvsEwNFsOsktQ05C_hwn41Ci6MIjIXP6f9MBhOz96i6d-KeRuOaeMVH7UYjwA/s1600/osn.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="155" data-original-width="325" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh64CCkj8xxpZdNEBKPZUFfzZ69viR9K4g-wCoHlgxqumUcAACWOi1pgEts9EYdKO8JFm9MJ6GmRAPoOtxvsEwNFsOsktQ05C_hwn41Ci6MIjIXP6f9MBhOz96i6d-KeRuOaeMVH7UYjwA/s320/osn.jpg" width="320" /></a></div>
MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com1tag:blogger.com,1999:blog-2038459976334560100.post-18282791157646000122018-01-25T12:19:00.003+07:002018-01-25T12:26:44.366+07:00Soal Uji Coba Ujian Nasional 2017-2018<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf18pz4sljPVc6PbEwK7p53EcLInXMtjQ_9tG2NCpDXBLAySI0k3a_gEQuHvAf1DQAsxiIun9XYeoJpCPxQiqt0nw-zeLG0yn_kp0XCZfi8pvAgVia64da_wTeY9wMhXKNbM4-bs1oSIY/s1600/LOGO-SUKSES-UN.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="109" data-original-width="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf18pz4sljPVc6PbEwK7p53EcLInXMtjQ_9tG2NCpDXBLAySI0k3a_gEQuHvAf1DQAsxiIun9XYeoJpCPxQiqt0nw-zeLG0yn_kp0XCZfi8pvAgVia64da_wTeY9wMhXKNbM4-bs1oSIY/s1600/LOGO-SUKSES-UN.jpg" /></a></div>
<br />
Soal Uji Coba UN<br />
<br />
Mapel Matematika SMK<br />
<br />
<br />
Soal Matematika <a href="http://swiftation.com/73g9" target="_blank">Seni pariwisata Kerumahtanggaan</a><br />
<br />
Soal Matematika <a href="http://swiftation.com/73qZ" target="_blank">Akutansi Penjualan</a><br />
<br />
Soal Matematika <a href="http://swiftation.com/73nm" target="_blank">Tekonologi Kesehatan Pertanian</a>MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-82143289974163566802017-10-27T14:10:00.001+07:002019-11-07T19:19:11.906+07:00Kisi Kisi UAS/ PAS gasal Matematika SMK tahun 2017-2018Kisi - kisi Penlaian Akhir Semester Gasal Matematika SMK<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShxWedoBGd5J0PBwFpOBdEWljnrHqR-AvzrQjUJWdDDcwyI965EsQC-tcwJ5C8fPMcCy2dIZCLxIe3NtOQKffHU3H-HAkAcFPo_90M49MqJ_0oeZib4c_y7blYg2ct11fTrKZwLS_F4Kq/s1600/images.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="137" data-original-width="368" height="119" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShxWedoBGd5J0PBwFpOBdEWljnrHqR-AvzrQjUJWdDDcwyI965EsQC-tcwJ5C8fPMcCy2dIZCLxIe3NtOQKffHU3H-HAkAcFPo_90M49MqJ_0oeZib4c_y7blYg2ct11fTrKZwLS_F4Kq/s320/images.png" width="320" /></a></div>
<br />
silahkan di download kisi-kisi soal penilaian khir semester gasal<br />
<br />
ada dua kurikulum yang berlaku untuk kelas XI dan XII yakni KTSP dan K-13<br />
sedangkan untuk kelas X menggunakan kurikulum K-13 semua program keahlian<br />
<br />
1. Kelas X (<a href="http://twineer.com/7Rb1" target="_blank">K-13 semua jurusan</a> )<br />
<br />
2. kelas XI - <a href="http://twineer.com/7RY9" target="_blank">K 13</a><br />
- <a href="http://twineer.com/7RDb" target="_blank">Teknik (KTSP)</a><br />
- <a href="http://twineer.com/7RUP" target="_blank">Non teknik (KTSP)</a><br />
<br />
3. Kelas XII (KTSP dan K-13)<br />
- <a href="http://twineer.com/7Rcb" target="_blank">TKP (Teknik Kesehatan dan Pertanian )</a><br />
- <a href="http://twineer.com/7Rdn" target="_blank">AP, PJ (Akutansi dan Penjualan )</a><br />
- <a href="http://twineer.com/7Rf5" target="_blank">PSK (Pariwisata seni kerumahtanggaan )</a><br />
<br />
Kisi-kisi UAS Gasal tahun 2019-2020 <a href="https://mgmp-mat-smk-byl.blogspot.com/2019/11/kisi-kisi-pas-gasal-2019-2020.html" target="_blank">disini</a>Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-14207367994288946872017-10-15T13:20:00.000+07:002017-10-15T13:20:50.517+07:00Menggambar Grafik dengan Google<div class="article-header" style="background-color: white; display: table; font-family: "Helvetica Neue Light", HelveticaNeue-Light, "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin: 0px; outline: none; padding: 0px; text-align: center; width: 750px;">
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Kabar gembira terutama terutama buat kalian yang masih pelajar. Sekarang kalian tidak perlu repot-repot menggunakan <a href="http://www.wolframalpha.com/" style="color: #4ba976; display: inline; outline: none; text-decoration-line: none; transition: color 0.3s;">WolframAlpha</a> untuk membantu menggambar grafik. Karena Google juga telah mampu untuk menggambar grafik fungsi matematika. Cukup ketikkan fungsi yang kalian inginkan dan secara ajaib tapi nyata Mbah Google akan langsung menggambarkan grafiknya untuk kalian. Saat saya coba Google mampu untuk menggambar grafik polinom, eksponensial, trigonometri dan lograritma. Bahkan kita dapat menggambar 2 grafik atau lebih dengan memisahkannya dengan tanda koma serta memperbesar (zoom) dan menggeser (pan) grafik tersebut. Sayangnya untuk saat ini Google hanya mampu menggambar grafik 2 dimensi (x,y) semoga untuk kedepannya fitur grafik 3 dimensi (x,y,z) dapat ditambahkan.</h4>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRm0sAcjdqSZk7nQEIIuW0k4YAvWhgeGU9byx3X0rNuC-HUtBVRp7yd2uN-GyZDWRbk-OZR9-ugChKQQGsaO5nbS7X_Ovjtza_Ie1AVmCswRrVaoj7WQsY_JTyWlDANJTvdQbCkxVYimIN/s640/equation.png" imageanchor="1" style="color: #4ba976; display: inline; margin-left: 1em; margin-right: 1em; outline: none; text-decoration-line: none; transition: color 0.3s;"><img border="0" height="326" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRm0sAcjdqSZk7nQEIIuW0k4YAvWhgeGU9byx3X0rNuC-HUtBVRp7yd2uN-GyZDWRbk-OZR9-ugChKQQGsaO5nbS7X_Ovjtza_Ie1AVmCswRrVaoj7WQsY_JTyWlDANJTvdQbCkxVYimIN/s400/equation.png" style="-webkit-border-image: url("data:image/png; border: 9px none; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; position: relative;" width="400" /></a></div>
<br /><h5 style="font-weight: bolder; margin: 1.5em 0px; padding: 0px;">
Artikel dari Google mengenai pengumuman fitur ini : <a href="http://insidesearch.blogspot.com/2011/12/showing-some-love-to-math-lovers.html" style="color: #4ba976; display: inline; outline: none; text-decoration-line: none; transition: color 0.3s;">"Showing Some Love to Math Lover</a></h5>
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Oh ya, coba kalian ketik <a href="https://www.google.com/search?ie=UTF-8&q=%28sqrt%28cos%28x%29%29*cos%28200x%29%2Bsqrt%28abs%28x%29%29-0.7%29*%284-x*x%29%5E0.01%2C+sqrt%289-x%5E2%29%2C+-sqrt%289-x%5E2%29+from+-4.5+to+4.5" style="color: #4ba976; display: inline; outline: none; transition: color 0.3s;">(sqrt(cos(x))*cos(200x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(9-x^2), -sqrt(9-x^2) from -4.5 to 4.5 </a>di kolom pencarian Google dan lihat apa yang terjadi, :D</h5>
</div>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-77351602951056861042017-10-15T13:10:00.000+07:002017-10-15T13:15:33.746+07:00Kalkulus edisi 9: Purcell, Varberg, Rigdon<div class="article-header" style="background-color: white; display: table; font-family: "Helvetica Neue Light", HelveticaNeue-Light, "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin: 0px; outline: none; padding: 0px; text-align: center; width: 750px;">
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</h4>
<div>
<br /></div>
<div>
Download <a href="http://yobuilder.com/ADqU" target="_blank">disini</a><br />
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Kunci jawaban soal soal pada buku ini dapat <a href="http://yobuilder.com/ADtD" target="_blank">Download disini</a><br />
<h1 class="title entry-title" itemprop="name" style="display: table-cell; font-size: 20px; font-weight: normal; margin: 0px; padding: 0px 40px 0px 0px; position: relative; text-align: center; vertical-align: middle; width: 710px;">
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</h1>
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Buku lain: </div>
<ul style="font-family: Arial, serif; font-size: 14.3px; text-align: left;">
<li><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" style="color: #fc8901;" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
<li><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/kalkulus-dasar-10.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">Kalkulus dsar 1.0 untuk SMA dan Awal universitas</a></li>
<li><span style="font-family: "arial" , serif;"><span style="font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/100-great-problems-of-elementary.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">100 Great Problems of Elementary Mathematics - Heinrich Dorrie</a></span></span></li>
</ul>
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Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-81520794094682038412017-10-10T06:14:00.000+07:002017-10-10T06:14:06.360+07:00A First Course in Noncommutative Rings 2001 Tsit-Yuen LamA First Course in Noncommutative Rings 2001 Tsit-Yuen Lam<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwTmZrnPH2WI6iRmtV07uw2rlvCVxiPGXSRh_28W4wqOQxGGXC9Vwug1w_HZ9809W0owU_zTuFKhPuQ3-xowqzwQhUGKJpxdbQ21LiGQ0nlkE-Bn6aSSYnbJHNRXjVmfxKtBYQsLTlvTTj/s1600/41bOidWVpBL._SX327_BO1%252C204%252C203%252C200_.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="329" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwTmZrnPH2WI6iRmtV07uw2rlvCVxiPGXSRh_28W4wqOQxGGXC9Vwug1w_HZ9809W0owU_zTuFKhPuQ3-xowqzwQhUGKJpxdbQ21LiGQ0nlkE-Bn6aSSYnbJHNRXjVmfxKtBYQsLTlvTTj/s320/41bOidWVpBL._SX327_BO1%252C204%252C203%252C200_.jpg" width="210" /></a></div>
<br />
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<a href="http://yobuilder.com/1oyX" target="_blank">Download disini</a><br />
<br />
<span style="background-color: white; color: #333333; font-family: arial, serif; font-size: 14.3px;">Buku Lain :</span><br />
<ul style="background-color: white; color: #333333; font-family: Arial, serif; font-size: 14.3px;">
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/kalkulus-dasar-10.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">Kalkulus dsar 1.0 untuk SMA dan Awal universitas</a></li>
<li><span style="font-family: arial, serif;"><span style="font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/100-great-problems-of-elementary.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">100 Great Problems of Elementary Mathematics - Heinrich Dorrie</a></span></span></li>
</ul>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-79178547031721065002017-10-10T04:50:00.001+07:002017-10-10T04:51:32.363+07:00104 Number Theory Problems_Titu Andreescu, Dorin Andrica and Zuming Feng104 Number Theory Problems_Titu Andreescu, Dorin Andrica and Zuming Feng<br />
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<div class="separator" style="clear: both; text-align: center;">
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<br />
<a href="http://yobuilder.com/1icr" target="_blank">download disini</a><br />
<br />
<span style="background-color: white; color: #333333; font-family: "arial" , serif; font-size: 14.3px;">Buku Lain :</span><br />
<ul style="background-color: white; color: #333333; font-family: Arial, serif; font-size: 14.3px;">
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" style="color: #fc8901;" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
<li style="font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/kalkulus-dasar-10.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">Kalkulus dsar 1.0 untuk SMA dan Awal universitas</a></li>
<li><span style="font-family: "arial" , serif;"><span style="font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/100-great-problems-of-elementary.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">100 Great Problems of Elementary Mathematics - Heinrich Dorrie</a></span></span></li>
</ul>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-74528276600393323592017-10-09T22:02:00.000+07:002017-10-09T22:04:18.418+07:00100 Great Problems of Elementary Mathematics - Heinrich Dorrie<div class="separator" style="clear: both; text-align: center;">
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<span style="background-color: white; color: #333333; font-family: "arial" , serif; font-size: 14.3px;">Buku Lain :</span><br />
<ul style="background-color: white;">
<li style="color: #333333; font-family: arial, serif; font-size: 14.3px;"><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" style="color: #fc8901;" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li style="color: #333333; font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
<li style="color: #333333; font-family: arial, serif; font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/kalkulus-dasar-10.html" style="color: #fc8901; text-decoration-line: none;" target="_blank">Kalkulus dsar 1.0 untuk SMA dan Awal universitas</a></li>
<li><span style="color: #333333; font-family: arial, serif;"><span style="font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/100-great-problems-of-elementary.html" target="_blank">100 Great Problems of Elementary Mathematics - Heinrich Dorrie</a></span></span></li>
</ul>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-8592088330226194292017-10-09T20:24:00.001+07:002017-10-09T20:24:10.308+07:00BUKU GURU DAN BUKU SISWA KURIKULUM 2017 Edisi Revisi 2017BUKU GURU DAN BUKU SISWA KURIKULUM 2017 Edisi Revisi 2017<br />
<br />
Pada kesempatan kali ini blog berbagi dan belajar akan membagikan link buku pelajaran kurikulum 2013 edisi revisi 2017. Buku-buku tersebut sebenarnya dapat diunduh di laman buku.kemdikbud.go.id dan blog berbagi dan belajar hanya membantu para pengunduh untuk memberikan alternatif alamat unduhan untuk buku kurikulum 2013 edisi 2017 baik buku siswa dan buku guru.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio2rvY2JPQsoE1eu0Yv1VDy0SBVryg26tpI6zR4HdXLOkn2Mmh7B2ztErIO2J2XASXDPjCqkzXc6lAlL5ztYsDrvX5GkD0M3jWf33s3KwlBCi1ghmKir3Zo8Q4NORPXYMHHJPNp1espaWD/s1600/download.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="160" data-original-width="315" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio2rvY2JPQsoE1eu0Yv1VDy0SBVryg26tpI6zR4HdXLOkn2Mmh7B2ztErIO2J2XASXDPjCqkzXc6lAlL5ztYsDrvX5GkD0M3jWf33s3KwlBCi1ghmKir3Zo8Q4NORPXYMHHJPNp1espaWD/s400/download.jpg" width="400" /></a></div>
<br />
<br />
Link yang akan dibagikan ini adalah berupa link google drive sehingga mudah untuk didownload. Buku-buku pelajaran kurikulum 2013 edisi revisi 2017 ini adalah untuk jenjang SMP/MTs dan SMA/MA/SMK/MAK.<br />
Klik link di bawah ini untuk mendownload.<br />
<br />
<a href="http://yobuilder.com/10z7" target="_blank">Download buku pelajaran kurikulum 2013 edisi revisi 2017</a><br />
<br />
Semoga bermanfaatMatematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-25708510131599774982017-10-09T15:56:00.000+07:002017-10-09T22:04:37.263+07:00Kalkulus Dasar 1.0<div class="separator" style="clear: both; text-align: center;">
<a href="http://yobuilder.com/gn8" target="_blank"><img border="0" data-original-height="520" data-original-width="398" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC_7eIwMIx64T69pmSBuGFts54Qs4huj6dzH566BFD_qq64Yv03mIgkYOyVwLW7heM4Xtp1UuwAGnTMceOWWX8Xe7bAsdv119twVLLxaLbS10H3va_5KIYeU2pqQZTwRjvGcBwq8Mb-KBx/s320/kalkulus+dasar.jpg" width="244" /></a></div>
<br />
<a href="http://yobuilder.com/gn8" target="_blank">Download disini </a><br />
<br />
Buku Lain :<br />
<ul>
<li><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
<li><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/kalkulus-dasar-10.html" target="_blank">Kalkulus dsar 1.0 untuk SMA dan Awal universitas</a></li>
<li><span style="color: #333333; font-family: arial, serif;"><span style="font-size: 14.3px;"><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/100-great-problems-of-elementary.html" target="_blank">100 Great Problems of Elementary Mathematics - Heinrich Dorrie</a></span></span></li>
</ul>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com1tag:blogger.com,1999:blog-2038459976334560100.post-15311017500364882232017-10-09T06:01:00.000+07:002017-10-09T06:01:02.452+07:00Download laporan Nilai Hasil UKG Tahun 2015<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
Beberapa waktu yang lalu pastinya Anda yang membuka website ini sudah mengikuti sebuah penilaian guru yaitu Uji Kompetensi Guru atau biasa kita sebut UKG. Tepatnya UKG Tahun 2015 Anda sudah diuji dan sudah tahu pastinya hasilnya bukan?</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWBh7QMZvzfXNkZjR62Kd3mjcdMRaWVjaO6OHB3zkCViWPYR8tB7JL5Pu9E0_uK5weGDA4Qftkue4e6Km8a22ITeJ8363XtOVIPOCXsDtD9x2a7FiCKfcZ6Fk3dc2NXN3c-Tuh3LV88t16/s1600/nilai+ukg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="567" data-original-width="1277" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWBh7QMZvzfXNkZjR62Kd3mjcdMRaWVjaO6OHB3zkCViWPYR8tB7JL5Pu9E0_uK5weGDA4Qftkue4e6Km8a22ITeJ8363XtOVIPOCXsDtD9x2a7FiCKfcZ6Fk3dc2NXN3c-Tuh3LV88t16/s640/nilai+ukg.png" width="640" /></a></div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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Kompetensi dasar bidang studi yang diujikan sesuai dengan bidang studi sertifikasi (bagi guru yang sudah bersertifikat pendidik) dan sesuai dengan kualifikasi akademik guru (bagi guru yang belum bersertifikat pendidik). Kompetensi pedagogik yang diujikan adalah integrasi konsep pedagogik ke dalam proses pembelajaran bidang studi tersebut dalam kelas, bagi rekan - rekan guru yang ingin mengetahui nilai UKG nya silahkan download filenya di bawah ini :</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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<a href="http://quamiller.com/Bpzm" target="_blank">nilai UKG 2015</a></div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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semoga bermanfaat</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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<div style="background-color: white; border: 0px; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; font-stretch: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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<span style="background-color: white; color: #333333; font-family: Georgia, Utopia, "Palatino Linotype", Palatino, serif; font-size: 16px; text-align: justify;"><br /></span>Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-36974625279464937442017-10-08T22:14:00.001+07:002017-10-09T15:59:06.557+07:00Pembagian Materi Kelas X dan XI hasil MGMP<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 618px;">
<colgroup><col style="mso-width-alt: 1645; mso-width-source: userset; width: 34pt;" width="45"></col>
<col style="mso-width-alt: 1426; mso-width-source: userset; width: 29pt;" width="39"></col>
<col style="mso-width-alt: 4754; mso-width-source: userset; width: 98pt;" width="130"></col>
<col style="mso-width-alt: 4205; mso-width-source: userset; width: 86pt;" width="115"></col>
<col style="mso-width-alt: 4608; mso-width-source: userset; width: 95pt;" width="126"></col>
<col style="mso-width-alt: 5961; mso-width-source: userset; width: 122pt;" width="163"></col>
</colgroup><tbody>
<tr height="21" style="height: 15.75pt;">
<td class="xl75" height="21" style="height: 15.75pt; width: 34pt;" width="45">KELAS</td>
<td class="xl76" style="width: 29pt;" width="39">SMT</td>
<td class="xl77" style="width: 98pt;" width="130">KTSP TI</td>
<td class="xl76" style="width: 86pt;" width="115">KTSP BM</td>
<td class="xl77" style="width: 95pt;" width="126">KTSP PARIWISATA</td>
<td class="xl78" style="width: 122pt;" width="163">K 13</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl65" height="20" style="border-top: none; height: 15.0pt;">XII</td>
<td class="xl71" style="border-top: none;">5</td>
<td class="xl79" style="border-top: none;">Statistika</td>
<td class="xl80" style="border-top: none;">Statistika</td>
<td class="xl80" style="border-left: none; border-top: none;">Statistika</td>
<td class="xl81" style="border-top: none;">Metrik</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72">5</td>
<td>Limit Dan Turunan</td>
<td class="xl73">Hitung Keuangan</td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Bunga Pertumbuhan </td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72">5</td>
<td>Integral</td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Induksi Matematika</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Dimensi 3</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Integral</td>
</tr>
<tr height="21" style="height: 15.75pt;">
<td class="xl82" height="21" style="height: 15.75pt;"></td>
<td class="xl83"></td>
<td class="xl69"></td>
<td class="xl74"></td>
<td class="xl74" style="border-left: none;"></td>
<td class="xl70"></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;">XI</td>
<td class="xl72">3</td>
<td>Barisan Dan Deret</td>
<td class="xl73">Relasi Dan Fungsi</td>
<td class="xl73" style="border-left: none;">Relasi Dan Fungsi</td>
<td class="xl67">Program Linier</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td>Geometri Dimensi 2</td>
<td class="xl73">Geometri Dimensi 2</td>
<td class="xl73" style="border-left: none;">Geometri Dimensi 2</td>
<td class="xl67">Geometri Transformasi</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td>Geometri Dimensi 3</td>
<td class="xl73">Geometri Dimensi 3</td>
<td class="xl73" style="border-left: none;">Geometri Dimensi 3</td>
<td class="xl67">Rumus-Rumus Segitiga</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td>Vektor</td>
<td class="xl73">Trigonometri</td>
<td class="xl73" style="border-left: none;">Trigonometri</td>
<td class="xl67">Deret Tak Hingga</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Hubungan Garis</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Matrik</td>
</tr>
<tr height="21" style="height: 15.75pt;">
<td class="xl66" height="21" style="height: 15.75pt;"></td>
<td class="xl72"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67"></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl71">4</td>
<td class="xl79">Peluang</td>
<td class="xl80">Peluang</td>
<td class="xl80" style="border-left: none;">Peluang</td>
<td class="xl81">Statistik</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl72"></td>
<td>Irisan Kerucut</td>
<td class="xl73">Program Linier</td>
<td class="xl73" style="border-left: none;">Program Linier</td>
<td class="xl67">Peluang</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl73"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Komposisi Fungsi</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl73"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Limit</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl66" height="20" style="height: 15.0pt;"></td>
<td class="xl73"></td>
<td></td>
<td class="xl73"></td>
<td class="xl73" style="border-left: none;"></td>
<td class="xl67">Turunan</td>
</tr>
<tr height="21" style="height: 15.75pt;">
<td class="xl68" height="21" style="height: 15.75pt;"></td>
<td class="xl74"></td>
<td class="xl69"></td>
<td class="xl74"></td>
<td class="xl74" style="border-left: none;"></td>
<td class="xl70">Integral</td>
</tr>
</tbody></table>
<br />
<br />
<a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/09/kisi-kisi-un-smk-20172018.html" target="_blank">Kisi kisi UN Tahun 2017 di download disini</a>Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-2591301119674884002017-10-01T20:01:00.002+07:002017-10-01T20:25:28.148+07:00MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)<div class="separator" style="clear: both; text-align: center;">
<a href="http://quainator.com/8wCe" target="_blank"><img border="0" data-original-height="629" data-original-width="468" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIZ6m-pD6Pkjru8KvtPPQSCGOQ5c_fjtWgCB5BmHGajj6OfnAMSKx14jMICjvDwx5PYee6tfJgBeo8zVsvqPsLmuPcbsWpWeB1MikILAWZvH1IGTmrehz1sQVzE5D48O5B3xbv4A4QRBM/s320/Mathematics+for+Machine+Technology+4th+Edition.jpg" width="238" /></a></div>
<br />
<a href="http://quainator.com/8wCe" target="_blank">download klik disini </a><br />
<br />
buku lain :<br />
<br />
<ul>
<li><a href="https://mgmp-mat-smk-byl.blogspot.co.id/2013/01/kalkulus-dan-geometri-analitis-edwin-j.html" target="_blank">Kalkulus dan Geometri Analitis - Edwin J. Purcell dan Dale Varbeg</a></li>
<li><a href="http://mgmp-mat-smk-byl.blogspot.co.id/2017/10/mathematics-for-machine-technology.html" target="_blank">MATHEMATICS FOR MACHINE TECHNOLOGY - Robert Donald Smith (4 edition)</a></li>
</ul>
<ul>
</ul>
MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-48996659783776967892017-09-29T21:56:00.002+07:002017-09-29T21:57:57.131+07:00Kata Kerja Operasional<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsVvCUgFtXGA27xAZZ1NIsHuwARNrOMSGueSjVBXj0VJViQ9dIjL4VfwKTdJufUPi5xnXqs8wbI657S8nWDUAIs0zEXXB20taJi0v13lNVPKCrD7MUKfMpcLNWmR5zjIm_mbOky248OuY/s1600/images+%25283%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="202" data-original-width="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsVvCUgFtXGA27xAZZ1NIsHuwARNrOMSGueSjVBXj0VJViQ9dIjL4VfwKTdJufUPi5xnXqs8wbI657S8nWDUAIs0zEXXB20taJi0v13lNVPKCrD7MUKfMpcLNWmR5zjIm_mbOky248OuY/s1600/images+%25283%2529.jpg" /></a></div>
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<table border="1" cellpadding="0" cellspacing="0" style="color: black; width: 904px;"><thead>
<tr><td width="97"><div align="center">
<strong>Pengetahuan</strong></div>
<div align="center">
<strong>C1</strong></div>
</td><td width="102"><div align="center">
<strong>Pemahaman</strong></div>
<div align="center">
<strong>C2</strong></div>
</td><td width="96"><div align="center">
<strong>Penerapan</strong></div>
<div align="center">
<strong>C3</strong></div>
</td><td width="94"><div align="center">
<strong>Analisis</strong></div>
<div align="center">
<strong>C4</strong></div>
</td><td width="112"><div align="center">
<strong>Sintesis</strong></div>
<div align="center">
<strong>C5</strong></div>
</td><td width="102"><div align="center">
<strong>Penilaian</strong></div>
<div align="center">
<strong>C6</strong></div>
</td></tr>
</thead><tbody>
<tr class="odd"><td valign="top" width="97">MengutipMenyebutkanMenjelaskan<br />
Menggambar<br />
Membilang<br />
Mengidentifikasi<br />
Mendaftar<br />
Menunjukkan<br />
Memberi label<br />
Memberi indeks<br />
Memasangkan<br />
Menamai<br />
Menandai<br />
Membaca<br />
Menyadari<br />
Menghafal<br />
Meniru<br />
Mencatat<br />
Mengulang<br />
Mereproduksi<br />
Meninjau<br />
Memilih<br />
Menyatakan<br />
Mempelajari<br />
Mentabulasi<br />
Memberi kode<br />
Menelusuri<br />
Menulis</td><td valign="top" width="102">MemperkirakanMenjelaskanMengkategorikan<br />
Mencirikan<br />
Merinci<br />
Mengasosiasikan<br />
Membandingkan<br />
Menghitung<br />
Mengkontraskan<br />
Mengubah<br />
Mempertahankan<br />
Menguraikan<br />
Menjalin<br />
Membedakan<br />
Mendiskusikan<br />
Menggali<br />
Mencontohkan<br />
Menerangkan<br />
Mengemukakan<br />
Mempolakan<br />
Memperluas<br />
Menyimpulkan<br />
Meramalkan<br />
Merangkum<br />
Menjabarkan</td><td valign="top" width="96">MenugaskanMengurutkanMenentukan<br />
Menerapkan<br />
Menyesuaikan<br />
Mengkalkulasi<br />
Memodifikasi<br />
Mengklasifikasi<br />
Menghitung<br />
Membangun<br />
Membiasakan<br />
Mencegah<br />
Menentukan<br />
Menggambarkan<br />
Menggunakan<br />
Menilai<br />
Melatih<br />
Menggali<br />
Mengemukakan<br />
Mengadaptasi<br />
Menyelidiki<br />
Mengoperasikan<br />
Mempersoalkan<br />
Mengkonsepkan<br />
Melaksanakan<br />
Meramalkan<br />
Memproduksi<br />
Memproses<br />
Mengaitkan<br />
Menyusun<br />
Mensimulasikan<br />
Memecahkan<br />
Melakukan<br />
Mentabulasi<br />
Memproses<br />
Meramalkan</td><td valign="top" width="94">MenganalisisMengauditMemecahkan<br />
Menegaskan<br />
Mendeteksi<br />
Mendiagnosis<br />
Menyeleksi<br />
Merinci<br />
Menominasikan<br />
Mendiagramkan<br />
Megkorelasikan<br />
Merasionalkan<br />
Menguji<br />
Mencerahkan<br />
Menjelajah<br />
Membagankan<br />
Menyimpulkan<br />
Menemukan<br />
Menelaah<br />
Memaksimalkan<br />
Memerintahkan<br />
Mengedit<br />
Mengaitkan<br />
Memilih<br />
Mengukur<br />
Melatih<br />
Mentransfer</td><td valign="top" width="112">MengabstraksiMengaturMenganimasi<br />
Mengumpulkan<br />
Mengkategorikan<br />
Mengkode<br />
Mengombinasikan<br />
Menyusun<br />
Mengarang<br />
Membangun<br />
Menanggulangi<br />
Menghubungkan<br />
Menciptakan<br />
Mengkreasikan<br />
Mengoreksi<br />
Merancang<br />
Merencanakan<br />
Mendikte<br />
Meningkatkan<br />
Memperjelas<br />
Memfasilitasi<br />
Membentuk<br />
Merumuskan<br />
Menggeneralisasi<br />
Menggabungkan<br />
Memadukan<br />
Membatas<br />
Mereparasi<br />
Menampilkan<br />
Menyiapkan Memproduksi<br />
Merangkum<br />
Merekonstruksi</td><td valign="top" width="102">MembandingkanMenyimpulkanMenilai<br />
Mengarahkan<br />
Mengkritik<br />
Menimbang<br />
Memutuskan<br />
Memisahkan<br />
Memprediksi<br />
Memperjelas<br />
Menugaskan<br />
Menafsirkan<br />
Mempertahankan<br />
Memerinci<br />
Mengukur<br />
Merangkum<br />
Membuktikan<br />
Memvalidasi<br />
Mengetes<br />
Mendukung<br />
Memilih<br />
Memproyeksikan<br />
<br /></td></tr>
</tbody></table>
<br />
<div>
Tabel 2. Kata Kerja Ranah Afektif</div>
<table border="1" cellpadding="0" cellspacing="0" style="color: black; width: 783px;"><tbody>
<tr><td width="127"><div align="center">
<strong>Menerima</strong></div>
<div align="center">
<strong>A1</strong></div>
</td><td width="120"><div align="center">
<strong>Menanggapi</strong></div>
<div align="center">
<strong>A2</strong></div>
</td><td width="110"><div align="center">
<strong>Menilai</strong></div>
<div align="center">
<strong>A3</strong></div>
</td><td width="118"><div align="center">
<strong>Mengelola</strong></div>
<div align="center">
<strong>A4</strong></div>
</td><td width="125"><div align="center">
<strong>Menghayati</strong></div>
<div align="center">
<strong>A5</strong></div>
</td></tr>
<tr class="odd"><td valign="top" width="127">MemilihMempertanyakanMengikuti<br />
Memberi<br />
Menganut<br />
Mematuhi<br />
Meminati</td><td valign="top" width="120">MenjawabMembantuMengajukan<br />
Mengompromikan<br />
Menyenangi<br />
Menyambut<br />
Mendukung<br />
Menyetujui<br />
Menampilkan<br />
Melaporkan<br />
Memilih<br />
Mengatakan<br />
Memilah<br />
Menolak</td><td valign="top" width="110">MengasumsikanMeyakiniMelengkapi<br />
Meyakinkan<br />
Memperjelas<br />
Memprakarsai<br />
Mengimani<br />
Mengundang<br />
Menggabungkan<br />
Mengusulkan<br />
Menekankan<br />
Menyumbang</td><td valign="top" width="118">MenganutMengubahMenata<br />
Mengklasifikasikan<br />
Mengombinasikan<br />
Mempertahankan<br />
Membangun<br />
Membentuk pendapat<br />
Memadukan<br />
Mengelola<br />
Menegosiasi<br />
Merembuk</td><td valign="top" width="125">Mengubah perilakuBerakhlak muliaMempengaruhi<br />
Mendengarkan<br />
Mengkualifikasi<br />
Melayani<br />
Menunjukkan<br />
Membuktikan<br />
Memecahkan</td></tr>
</tbody></table>
<br />
<div>
Tabel 3. Kata Kerja Ranah Psikomotorik</div>
<table border="1" cellpadding="0" cellspacing="0" style="color: black; width: 783px;"><tbody>
<tr><td width="168"><div align="center">
<strong>Menirukan</strong></div>
<div align="center">
<strong>P1</strong></div>
</td><td width="148"><div align="center">
<strong>Memanipulasi</strong></div>
<div align="center">
<strong>P2</strong></div>
</td><td width="142"><div align="center">
<strong>Pengalamiahan</strong></div>
<div align="center">
<strong>P3</strong></div>
</td><td width="135"><div align="center">
<strong>Artikulasi</strong></div>
<div align="center">
<strong>P4</strong></div>
</td></tr>
<tr class="odd"><td valign="top" width="168">MengaktifkanMenyesuaikanMenggabungkan<br />
Melamar<br />
Mengatur<br />
Mengumpulkan<br />
Menimbang<br />
Memperkecil<br />
Membangun<br />
Mengubah<br />
Membersihkan<br />
Memposisikan<br />
Mengonstruksi</td><td valign="top" width="148">MengoreksiMendemonstrasikanMerancang<br />
Memilah<br />
Melatih<br />
Memperbaiki<br />
Mengidentifikasikan<br />
Mengisi<br />
Menempatkan<br />
Membuat<br />
Memanipulasi<br />
Mereparasi<br />
Mencampur</td><td valign="top" width="142">MengalihkanMenggantikanMemutar<br />
Mengirim<br />
Memindahkan<br />
Mendorong<br />
Menarik<br />
Memproduksi<br />
Mencampur<br />
Mengoperasikan<br />
Mengemas<br />
Membungkus</td><td valign="top" width="135">MengalihkanMempertajamMembentuk<br />
Memadankan<br />
Menggunakan<br />
Memulai<br />
Menyetir<br />
Menjeniskan<br />
Menempel<br />
Menseketsa<br />
Melonggarkan<br />
Menimbang</td></tr>
</tbody></table>
<br />
<div>
Tabel 4. Tingkat Kompetensi Kata Kerja Operasional</div>
<br />
<table border="1" cellpadding="0" cellspacing="0" style="color: black; width: 783px;"><thead>
<tr><td width="36"><div align="center">
No</div>
</td><td width="108">Klasifikasi Tingkat Kompetensi</td><td width="425">Kata Kerja Operasional yang Digunakan</td></tr>
</thead><tbody>
<tr class="odd"><td valign="top" width="36"><div align="center">
1</div>
</td><td valign="top" width="108">Berhubungan dengan mencari keterangan (<em>dealing with retrieval</em>) </td><td valign="top" width="425">1. Mendeskripsikan (<em>describe</em>)2. Menyebutkan kembali (<em>recall</em>)3. Melengkapi (<em>complete</em>)<br />
4. Mendaftar (<em>list</em>)<br />
5. Mendefinisikan (<em>define</em>)<br />
6. Menghitung (<em>count</em>)<br />
7. Mengidentifikasi (<em>identify</em>)<br />
8. Menceritakan (<em>recite</em>)<br />
9. Menamai (<em>name</em>)</td></tr>
<tr><td valign="top" width="36"><div align="center">
2</div>
</td><td valign="top" width="108">Memproses (processing) </td><td valign="top" width="425">1. Mensintesis (<em>synthesize</em>)2. Mengelompokkan (<em>group</em>)3. Menjelaskan (<em>explain</em>)<br />
4. Mengorganisasikan (<em>organize</em>)<br />
5. Meneliti/melakukan eksperimen (<em>experiment</em>)<br />
6. Menganalogikan (<em>make analogies</em>)<br />
7. Mengurutkan (<em>sequence</em>)<br />
8. Mengkategorikan (<em>categorize</em>)<br />
9. Menganalisis (<em>analyze</em>)<br />
10. Membandingkan (<em>compare</em>)<br />
11. Mengklasifikasi (<em>classify</em>)<br />
12. Menghubungkan (<em>relate</em>)<br />
13. Membedakan (<em>distinguish</em>)<br />
Mengungkapkan sebab (<em>state causality</em>)</td></tr>
<tr class="odd"><td valign="top" width="36"><div align="center">
3</div>
</td><td valign="top" width="108">Menerapkan dan mengevaluasi </td><td valign="top" width="425">1. Menerapkan suatu prinsip (<em>applying a principle</em>)2. Membuat model (<em>model building</em>)3. Mengevaluasi (<em>evaluating</em>)<br />
4. Merencanakan (<em>planning</em>)<br />
5. Memperhitungkan/meramalkan kemungkinan (<em>extrapolating</em>)<br />
6. Memprediksi (<em>predicting</em>)<br />
7. Menduga/Mengemukakan pendapat/ mengambil kesimpulan (<em>inferring</em>)<br />
8. Meramalkan kejadian alam/sesuatu (<em>forecasting</em>)<br />
9. Menggeneralisasikan (<em>generalizing</em>)<br />
10. Mempertimbangkan /memikirkan kemungkinan-kemungkinan (<em>speculating</em>)<br />
11. Membayangkan /mengkhayalkan/ mengimajinasikan (<em>Imagining</em>)<br />
12. Merancang (<em>designin</em>g)<br />
13. Menciptakan (<em>creating</em>)<br />
14. Menduga/membuat dugaan/ kesimpulan awal (<em>hypothezing</em>)</td></tr>
</tbody></table>
MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-12377208455454857052017-09-29T21:04:00.000+07:002017-09-29T21:49:12.397+07:00Bank soal UN tahun 2015-2016<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigjdCK0tjsVqbXNen65sx0VZ2RB6JxcJOLRQ0Wtf3LkxlfT7STl46eBtfSYJM_yrxFFhPPuVyV7u6ppoQZ-6qbGaLi8X2VTkem-AN_0afO4BPUush2eEe5MqN_vpz2AaWJQa_8rSvmY_8/s1600/soal+UN+2013.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="280" data-original-width="336" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigjdCK0tjsVqbXNen65sx0VZ2RB6JxcJOLRQ0Wtf3LkxlfT7STl46eBtfSYJM_yrxFFhPPuVyV7u6ppoQZ-6qbGaLi8X2VTkem-AN_0afO4BPUush2eEe5MqN_vpz2AaWJQa_8rSvmY_8/s320/soal+UN+2013.jpg" width="320" /></a></div>
<br />
Soal Prediksi FKGM 2015-2016<br />
<br />
Kelompok Bismen<br />
<br />
1. <a href="http://quainator.com/5yVJ" target="_blank">Paket 1</a><br />
2. <a href="http://quainator.com/60zz" target="_blank">Paket 2</a><br />
3. <a href="http://quainator.com/5ycV" target="_blank">Paket 3</a><br />
4. <a href="http://quainator.com/5yfB" target="_blank">Paket 4</a><br />
5.<a href="http://quainator.com/5yhL" target="_blank"> Paket 5</a><br />
<br />
Kelompok Pariwisata<br />
<a href="http://quainator.com/623r" target="_blank">1. Paket 1</a><br />
<a href="http://quainator.com/626D" target="_blank">2. Paket 2</a><br />
<a href="http://quainator.com/628G" target="_blank">3. Paket 3</a><br />
<a href="http://quainator.com/62AP" target="_blank">4. Paket 4</a><br />
<a href="http://quainator.com/62Bu" target="_blank">5. Paket 5</a><br />
<br />
<br />MGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-72204874812511094992017-09-29T20:22:00.000+07:002017-09-29T20:55:37.200+07:00Bank Soal UAS Gasal<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdZHZCCoyGrnkOsc7veRdScxhgzdfww37kXumPmHUCPd7fsbjYF7HgUj7ySL_DOukZ5W83wyQjAg6Bsx9wEsQQCF5hzS7Z6udkms9vsZR4_DL5dba33BTK7U8wzcovTADP6qRO1T1r4oY/s1600/images+%25282%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="157" data-original-width="321" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdZHZCCoyGrnkOsc7veRdScxhgzdfww37kXumPmHUCPd7fsbjYF7HgUj7ySL_DOukZ5W83wyQjAg6Bsx9wEsQQCF5hzS7Z6udkms9vsZR4_DL5dba33BTK7U8wzcovTADP6qRO1T1r4oY/s320/images+%25282%2529.jpg" width="320" /></a></div>
<br />
Silahkan downlaod soal-soal ulangan dibawah ini<br />
<br />
1. <a href="http://quainator.com/5vZS" target="_blank">Soal UAS Gasal kls X KTSP 2015-2016</a><br />
2. <a href="http://quainator.com/5vgt" target="_blank">Soal UAS Gasal kls XI KTSP 2015-2016</a><br />
3. <a href="http://quainator.com/5vt5" target="_blank">Soal UAS Gasal Kls XII TI dan K-13 tahun 2015-2016 paket A</a><br />
4. <a href="http://quainator.com/5vy0" target="_blank">Soal UAS Gasal Kls XII TI dan K-13 tahun 2015-2016 paket B</a><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYQ36SNnV8NmJ-2xBohABmZQ66hXejBJB1Iyr5H9jdY8GGhbNy09BE-eewMetWCGAiSdrrdEbux_UguPzOAXezasB9-mWXclt3Ff28vu-Fh_Ey6o3jCU8LRO-ScdqExuuYDaFgRBJIQqI/s1600/images+%25281%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="186" data-original-width="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYQ36SNnV8NmJ-2xBohABmZQ66hXejBJB1Iyr5H9jdY8GGhbNy09BE-eewMetWCGAiSdrrdEbux_UguPzOAXezasB9-mWXclt3Ff28vu-Fh_Ey6o3jCU8LRO-ScdqExuuYDaFgRBJIQqI/s1600/images+%25281%2529.jpg" /></a></div>
<br />
<a href="http://mgmp-mat-smk-byl.blogspot.co.id/2012/08/soal-soal-latihan-ujian-nasional.html" target="_blank">Bank Soal Ujian Nasional disini</a><br />
Prediksi FKGM tahun 2015-2016 disiniMGMP Matematika SMK Kab Boyolalihttp://www.blogger.com/profile/10494436102967351833noreply@blogger.com0tag:blogger.com,1999:blog-2038459976334560100.post-51638582493323046492017-09-10T11:46:00.003+07:002017-09-10T11:46:58.084+07:00Silabus SMK Terbaru Revisi 2017<h2>
<span style="font-weight: normal;">Silabus SMK Terbaru Revisi 2017</span></h2>
<h2>
<span style="font-weight: normal;">Silabus adalah elemen dari sistem kurikulum. Silabus, menurut Permendikbud No. 60 tahun 2014 tentang Kurikulum SMK, merupakan rencana pembelajaran pada suatu mata pelajaran yang mencakup Kompetensi Inti, Kompetensi Dasar, materi pembelajaran, kegiatan pembelajaran, penilaian, alokasi waktu, dan sumber belajar.</span></h2>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho7owJCN9a3fGwiIkdrCzdCyTkPZJ681ehJVeQGedaBYjlS3Svb6ZiJr1gRki-oa4D6QvjfAD4yacxQGKm22RvZSe0YuauC96YlfBZt6XcSmoLomAdj4JN_h6QNueOnf6TgwfPBJGlfyo0/s1600/silabus-300x143.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="143" data-original-width="300" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho7owJCN9a3fGwiIkdrCzdCyTkPZJ681ehJVeQGedaBYjlS3Svb6ZiJr1gRki-oa4D6QvjfAD4yacxQGKm22RvZSe0YuauC96YlfBZt6XcSmoLomAdj4JN_h6QNueOnf6TgwfPBJGlfyo0/s320/silabus-300x143.jpg" width="320" /></a></div>
<h2>
<span style="font-weight: normal;"><br /></span></h2>
<h2>
Pengertian Silabus</h2>
<h2>
<span style="font-weight: normal;">Silabus adalah bagian dari perencanaan pembelajaran pada suatu kelompok kompetensi atau mata pelajaran sebagai acuan penyusunan Rencana Pelaksanaan Pembelajaran (RPP) dan pelaksanaan pembelajaran. Silabus memuat rumusan kompetensi bidang keahlian masing-masing mata pelajaran yang mencakup kompetensi inti, kompetensi dasar, Indikator Pencapaian Kompetensi (IPK), materi pembelajaran, kegiatan pembelajaran, penilaian, alokasi waktu, dan sumber belajar.</span></h2>
<h2>
<span style="font-weight: normal;">Silabus SMK merupakan acuan penyusunan Rencana Pelaksanaan Pembelajaran (RPP) untuk setiap bahan kajian mata pelajaran di SMK. Walaupun hingga saat ini Direktorat Pembinaan SMK belum mengeluarkan silabus contoh kepada rekan pendidik di SMK, namun sesungguhnya Silabus SMK Terbaru Revisi 2017 dapat disusun sendiri oleh rekan-rekan pendidik SMK.</span></h2>
<h2>
<span style="font-weight: normal;"><br /></span></h2>
<h2>
Prinsip-prinsip Pengembangan Silabus</h2>
<h2>
<span style="font-weight: normal;">1.<span style="white-space: pre;"> </span>Ilmiah</span></h2>
<h2>
<span style="font-weight: normal;">Keseluruhan materi dan kegiatan pebelajaran yang menjadi muatan dalam silabus harus benar dan dapat dipertanggungjawabkan secara keilmuan.</span></h2>
<h2>
<span style="font-weight: normal;">2.<span style="white-space: pre;"> </span>Relevan</span></h2>
<h2>
<span style="font-weight: normal;">Cakupan, kedalaman, tingkat kesukaran dan urutan penyajian materi dalam silabus masing-masing mata pelajaran sesuai dengan tingkat perkembangan fisik, intelektual, sosial, emosional, spiritual peserta didik, dan level 2 dan 3 KKNI.</span></h2>
<h2>
<span style="font-weight: normal;">3.<span style="white-space: pre;"> </span>Sistematis</span></h2>
<h2>
<span style="font-weight: normal;">Komponen-komponen silabus saling berhubungan secara fungsional dalam pencapaian kompetensi inti sikap spiritual (KI-1), sikap sosial (KI-2), pengetahuan (KI-3), dan ketrampilan (KI-4). (Lihat Tabel 1, Tabel 2, Tabel 3, Tabel 4, Tabel 5 di atas).</span></h2>
<h2>
<span style="font-weight: normal;">4.<span style="white-space: pre;"> </span>Konsisten</span></h2>
<h2>
<span style="font-weight: normal;">Adanya hubungan yang konsisten (ajeg, taat asas) antara kompetensi dasar, indikator, materi pembelajaran, kegiatan pembelajaran, sumber belajar, dan sistem penilaian.</span></h2>
<h2>
<span style="font-weight: normal;">5.<span style="white-space: pre;"> </span>Memadai</span></h2>
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<span style="font-weight: normal;">Cakupan IPK, materi pembelajaran, kegiatan pembelajaran, sumber belajar, dan sistem penilaian memadai untuk menunjang pencapaian kompetensi dasar dan KI.</span></h2>
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<span style="font-weight: normal;">6.<span style="white-space: pre;"> </span>Aktual dan kontekstual</span></h2>
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<span style="font-weight: normal;">Cakupan IPK, materi pembelajaran, kegiatan pembelajaran, sumber belajar, dan sistem penilaian memperhatikan perkembangan ilmu, teknologi, dan seni mutakhir dalam kehidupan nyata, dan peristiwa yang terjadi di dunia kerja.</span></h2>
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<span style="font-weight: normal;">7.<span style="white-space: pre;"> </span>Fleksibel</span></h2>
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<span style="font-weight: normal;">Keseluruhan komponen silabus dapat mengakomodasi variasi peserta didik, pendidik, serta dinamika perubahan yang terjadi di sekolah dan tuntutan masyarakat.</span></h2>
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<span style="font-weight: normal;">8.<span style="white-space: pre;"> </span>Menyeluruh</span></h2>
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<span style="font-weight: normal;">Komponen silabus mencakup keseluruhan ranah kompetensi dimensi sikap spiritual, sosial, pengetahuan, dan ketrampilan (kognitif, afektif, dan psikomotor).</span></h2>
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<span style="font-weight: normal;">Langkah-langkah Pengembangan Silabus</span></h2>
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<span style="font-weight: normal;">Silabus seyogyanya dikembangkan mengikuti langkah-langkah pengembangan silabus seperti disajikan pada diagram alir berikut. Diagram Alir Pengembangan Silabus Mata Pelajaran.</span></h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8xalSM9bL-oKC40-EsQHdbQRyKBQSDH85QKWZOqO2Ggzj8Vl0buQ55MzJWK8EoZaPfFJPTUiR8TYDPeKAhcJRZIE73PodRW4pA6azSruHRYSwdx1TsVwVzCdIKL7AP3jBM0WhIGE_tQso/s1600/silabus-pengembangan-silabus.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="583" data-original-width="515" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8xalSM9bL-oKC40-EsQHdbQRyKBQSDH85QKWZOqO2Ggzj8Vl0buQ55MzJWK8EoZaPfFJPTUiR8TYDPeKAhcJRZIE73PodRW4pA6azSruHRYSwdx1TsVwVzCdIKL7AP3jBM0WhIGE_tQso/s640/silabus-pengembangan-silabus.jpg" width="564" /></a></div>
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<span style="font-weight: normal;"><br /></span></h2>
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<span style="font-weight: normal;"><a href="http://yoalizer.com/2ymn" target="_blank">silahkan download contoh silabus yang sudah diverifikasi</a></span></h2>
Matematikahttp://www.blogger.com/profile/02457970364409482535noreply@blogger.com0