1. limit x mendekati nol : sin4x tan² 3x + 6x³ per 2x² sin 3x cos 2x
2. limit x mendekati 3 : 1 - cos (x-3) per x² - 6x + 9
3. limit x mendekati 1 : sin (πx - π) per (x-1) cos (πx - π)
4. limit x mendekati ∞ : 2x -1 per 3 - x
2. limit x mendekati 3 : 1 - cos (x-3) per x² - 6x + 9
3. limit x mendekati 1 : sin (πx - π) per (x-1) cos (πx - π)
4. limit x mendekati ∞ : 2x -1 per 3 - x
Takamori37
![$\begin{align}\lim_{x\to0}\frac{\sin4x\tan^23x+6x^3}{2x^2\sin 3x\cos 2x}&=\lim_{x\to0}\frac{1}{\cos 2x}\times\lim_{x\to0}\frac{\sin4x\tan^23x+6x^3}{2x^2\sin3x} \\ &=\frac{1}{\cos 0}\left[\lim_{x\to0}\frac{\sin 4x\tan^23x}{2x^2\sin 3x}+\lim_{x\to0}\frac{6x^3}{2x^2\sin 3x}\right] \\ &=1\left[\frac{4\times 3^2}{2\times 3}+\frac{6}{2\times 3}\right] \\ &=\frac{4\times 3}{2}+\frac{6}{6} \\ &=6+1 \\ &=7\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin4x%5Ctan%5E23x%2B6x%5E3%7D%7B2x%5E2%5Csin+3x%5Ccos+2x%7D%26%3D%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B1%7D%7B%5Ccos+2x%7D%5Ctimes%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin4x%5Ctan%5E23x%2B6x%5E3%7D%7B2x%5E2%5Csin3x%7D+%5C%5C+%26%3D%5Cfrac%7B1%7D%7B%5Ccos+0%7D%5Cleft%5B%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csin+4x%5Ctan%5E23x%7D%7B2x%5E2%5Csin+3x%7D%2B%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B6x%5E3%7D%7B2x%5E2%5Csin+3x%7D%5Cright%5D+%5C%5C+%26%3D1%5Cleft%5B%5Cfrac%7B4%5Ctimes+3%5E2%7D%7B2%5Ctimes+3%7D%2B%5Cfrac%7B6%7D%7B2%5Ctimes+3%7D%5Cright%5D+%5C%5C+%26%3D%5Cfrac%7B4%5Ctimes+3%7D%7B2%7D%2B%5Cfrac%7B6%7D%7B6%7D+%5C%5C+%26%3D6%2B1+%5C%5C+%26%3D7%5Cend%7Balign%7D "$\begin{align}\lim_{x\to0}\frac{\sin4x\tan^23x+6x^3}{2x^2\sin 3x\cos 2x}&=\lim_{x\to0}\frac{1}{\cos 2x}\times\lim_{x\to0}\frac{\sin4x\tan^23x+6x^3}{2x^2\sin3x} \\ &=\frac{1}{\cos 0}\left[\lim_{x\to0}\frac{\sin 4x\tan^23x}{2x^2\sin 3x}+\lim_{x\to0}\frac{6x^3}{2x^2\sin 3x}\right] \\ &=1\left[\frac{4\times 3^2}{2\times 3}+\frac{6}{2\times 3}\right] \\ &=\frac{4\times 3}{2}+\frac{6}{6} \\ &=6+1 \\ &=7\end{align}")
![$\begin{align}\lim_{x\to3}\frac{1-\cos(x-3)}{x^2-6x+9}&=\lim_{x\to3}\frac{2\sin^2(\frac{x-3}{2})}{(x-3)^2} \\ &=2\left[\lim_{x\to3}\frac{\sin(\frac{x-3}{2})}{x-3}\right]^2 \\ &=2\left[\frac{1}{2}\right]^2 \\ &=2\times\frac{1}{4} \\ &=\frac{1}{2}\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Clim_%7Bx%5Cto3%7D%5Cfrac%7B1-%5Ccos%28x-3%29%7D%7Bx%5E2-6x%2B9%7D%26%3D%5Clim_%7Bx%5Cto3%7D%5Cfrac%7B2%5Csin%5E2%28%5Cfrac%7Bx-3%7D%7B2%7D%29%7D%7B%28x-3%29%5E2%7D+%5C%5C+%26%3D2%5Cleft%5B%5Clim_%7Bx%5Cto3%7D%5Cfrac%7B%5Csin%28%5Cfrac%7Bx-3%7D%7B2%7D%29%7D%7Bx-3%7D%5Cright%5D%5E2+%5C%5C+%26%3D2%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%5Cright%5D%5E2+%5C%5C+%26%3D2%5Ctimes%5Cfrac%7B1%7D%7B4%7D+%5C%5C+%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cend%7Balign%7D "$\begin{align}\lim_{x\to3}\frac{1-\cos(x-3)}{x^2-6x+9}&=\lim_{x\to3}\frac{2\sin^2(\frac{x-3}{2})}{(x-3)^2} \\ &=2\left[\lim_{x\to3}\frac{\sin(\frac{x-3}{2})}{x-3}\right]^2 \\ &=2\left[\frac{1}{2}\right]^2 \\ &=2\times\frac{1}{4} \\ &=\frac{1}{2}\end{align}")
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Elliemargartt
pinter bgt
ditajulia
kak, tolong jawab pertanyaan aku yang lain tentang limit ,, please
bayugaming1ouf24y
watafak
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