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: 35



Work Step by Step

$$\lim_{\theta\to0}\frac{\sin\theta}{\sin2\theta}=\lim_{\theta\to0}\frac{\sin\theta}{2\sin\theta\cos\theta}$$ $$\lim_{\theta\to0}\frac{\sin\theta}{\sin2\theta}=\lim_{\theta\to0}\frac{1}{2\cos\theta}$$ $$\lim_{\theta\to0}\frac{\sin\theta}{\sin2\theta}=\frac{1}{2\cos0}$$ $$\lim_{\theta\to0}\frac{\sin\theta}{\sin2\theta}=\frac{1}{2\times1}=\frac{1}{2}$$
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