Evaluate the following one sided limits: _ x 0^- (2- ) - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow0^-}(2-\cos\text{x})$

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Answer

$\lim\limits_{\text{x}\rightarrow0^-}(2-\cos\text{x})$
$\lim\limits_{\text{h}\rightarrow0}\ 2-\cot(0-\text{h})$
$=\lim\limits_{\text{h}\rightarrow0}\ 2-(-1)\cot\text{ h}$
$=\lim\limits_{\text{h}\rightarrow0}2+\cot\text{ h}$
$=\lim\limits_{\text{h}\rightarrow0}\ 2+\frac{1}{\tan\text{h}}$
$\Rightarrow2+\frac{1}{0}\Leftarrow\infty$

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