Answer
$\lim\limits_{x \to (\frac{\pi}{2})^+}\frac{1}{x}\sec x=-\infty$
Work Step by Step
$\lim\limits_{x \to (\frac{\pi}{2})^+}\frac{1}{x}\sec x=\frac{1}{(\frac{\pi}{2})^+} \sec(\frac{\pi}{2})^+=(\frac{2}{\pi}) \times-\infty=-\infty$
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