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: 11



Work Step by Step

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