Limit x mendekati 5 : (x-5) cotan (x-5)
Takamori37
![$\begin{align}\lim_{x\to5}(x-5)\cot(x-5)&=\lim_{x\to5}\frac{x-5}{\tan(x-5)} \\ &=\lim_{x\to5}\frac{x-5}{\sin(x-5)/\cos(x-5) \\ &=\lim_{x\to5}\left[\frac{x-5}{\sin(x-5)}\right]\times\lim_{x\to5}\frac{1}{\cos(x-5)}} \\ &=1\times\frac{1}{\cos(5-5)} \\ &=1\times\frac{1}{\cos 0}=1\times\frac{1}{1} \\ &=1\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Clim_%7Bx%5Cto5%7D%28x-5%29%5Ccot%28x-5%29%26%3D%5Clim_%7Bx%5Cto5%7D%5Cfrac%7Bx-5%7D%7B%5Ctan%28x-5%29%7D+%5C%5C+%26%3D%5Clim_%7Bx%5Cto5%7D%5Cfrac%7Bx-5%7D%7B%5Csin%28x-5%29%2F%5Ccos%28x-5%29+%5C%5C+%26%3D%5Clim_%7Bx%5Cto5%7D%5Cleft%5B%5Cfrac%7Bx-5%7D%7B%5Csin%28x-5%29%7D%5Cright%5D%5Ctimes%5Clim_%7Bx%5Cto5%7D%5Cfrac%7B1%7D%7B%5Ccos%28x-5%29%7D%7D+%5C%5C+%26%3D1%5Ctimes%5Cfrac%7B1%7D%7B%5Ccos%285-5%29%7D+%5C%5C+%26%3D1%5Ctimes%5Cfrac%7B1%7D%7B%5Ccos+0%7D%3D1%5Ctimes%5Cfrac%7B1%7D%7B1%7D+%5C%5C+%26%3D1%5Cend%7Balign%7D "$\begin{align}\lim_{x\to5}(x-5)\cot(x-5)&=\lim_{x\to5}\frac{x-5}{\tan(x-5)} \\ &=\lim_{x\to5}\frac{x-5}{\sin(x-5)/\cos(x-5) \\ &=\lim_{x\to5}\left[\frac{x-5}{\sin(x-5)}\right]\times\lim_{x\to5}\frac{1}{\cos(x-5)}} \\ &=1\times\frac{1}{\cos(5-5)} \\ &=1\times\frac{1}{\cos 0}=1\times\frac{1}{1} \\ &=1\end{align}")
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