University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 2 - Section 2.4 - One-Sided Limits - Exercises - Page 85: 34


$$\lim_{h\to0}\frac{\sin(\sin h)}{\sin h}=1$$

Work Step by Step

$$\lim_{h\to0}\frac{\sin(\sin h)}{\sin h}$$ Let's take $\theta=\sin h$ Then as $h\to0$, $\theta\to(\sin0)=0$ Therefore, $$\lim_{h\to0}\frac{\sin(\sin h)}{\sin h}=\lim_{\theta\to0}\frac{\sin\theta}{\theta}$$ Apply Theorem 7 here: $$\lim_{h\to0}\frac{\sin(\sin h)}{\sin h}=1$$
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