Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.6 Trigonometric Limits - Exercises - Page 77: 15



Work Step by Step

Since $-1\leq \cos (\tan \theta)\leq 1$, then we have $$-\cos \theta \leq\cos \theta \cos (\tan \theta)\leq\cos \theta.$$ Moreover, $\lim\limits_{\theta \to \frac{\pi}{2}} \cos\theta=\lim\limits_{\theta \to \frac{\pi}{2}}-\cos\theta=0$. Then by the Squeeze Theorem, we have $$\lim\limits_{\theta \to \frac{\pi}{2}}\cos \theta \cos (\tan \theta)=0.$$
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