Question
Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow\frac{\pi^-}{2}}\tan\text{x}$

Answer

$\lim\limits_{\text{x}\rightarrow\frac{\pi^-}{2}}\tan\text{ x}$
$=\lim\limits_{\text{h}\rightarrow0}\tan\big(\frac{\pi}{2}-\text{h}\big)$
$=\tan\big(\frac{\pi}{2}-0\big)$
$\Rightarrow\tan\frac{\pi}{2}=\infty$

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