Evaluate the given limit

by RoRi

September 2, 2015

Compute

$\lim_{x \to \frac{\pi}{2}} \frac{\sin (\cos x)}{\cos x}.$

Since cosine is continuous everywhere, we have

$\lim_{x \to \frac{\pi}{2}} \cos x = \cos \frac{\pi}{2} =0.$

Then, recalling that $\lim_{x \to 0} \frac{\sin x}{x} =1$ we have

$\lim_{x \to \frac{\pi}{2}} \frac{\sin (\cos x)}{\cos x} = 1.$

Stumbling Robot