University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises - Page 152: 54



Work Step by Step

$$A=\lim_{\theta\to0}\cos\Big(\frac{\pi\theta}{\sin\theta}\Big)$$ $$A=\cos\Big(\pi\lim_{\theta\to0}\frac{\theta}{\sin\theta}\Big)$$ Recall that $\lim_{x\to0}\frac{\sin x}{x}=1$ with $x=\theta$ here. $$A=\cos(\pi\times1)$$ $$A=\cos\pi=-1$$
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