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: 53


$$\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)=0$$

Work Step by Step

$$A=\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)$$ $$A=\tan\Big(1-\lim_{t\to0}\frac{\sin t}{t}\Big)$$ Recall that $\lim_{x\to0}\frac{\sin x}{x}=1$ with $x=t$ here. $$A=\tan(1-1)$$ $$A=\tan0=0$$
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