Evaluate the following one sided limits: _ x - 2^+ - Vidyadip

Question

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

✓

Answer

$\lim\limits_{\text{x}\rightarrow\frac{\pi^+}{2}}\sec\text{x}$
$=\lim\limits_{\text{h}\rightarrow0}\sec\big(-\frac{\pi}{2}+\text{h}\big)$
$=\sec\Big(-\frac{\pi}{2}+0\Big)$
$=\sec\Big(-\frac{\pi}{2}\Big)$
$=\frac{1}{\cos\Big(-\frac\pi2\Big)}$
$=\frac{-1}{\Big(\cos\frac{\pi}{2}\Big)}$
$\Rightarrow\frac{-1}{0}=-\infty$

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