Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.7 L'Hôpital's Rule - Exercises - Page 366: 33



Work Step by Step

We have $$ \lim _{x \rightarrow \frac{\pi}{2}} \frac{\cos x}{\sin 2 x}=\frac{0}{0} $$ is an intermediate form, then we can apply L’Hôpital’s Rule as follows $$ \lim _{x \rightarrow \frac{\pi}{2}} \frac{\cos x}{\sin 2 x}=\lim _{x \rightarrow \frac{\pi}{2}} \frac{-\sin x}{2\cos 2 x}=\frac{1}{2}. $$
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