Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - Chapter Review Exercises - Page 95: 47


$$\lim _{t \rightarrow 0+} \sqrt{t} \cos \left(\frac{1}{t}\right)=0$$

Work Step by Step

Since for $t>0$ $$-1 \leq \cos \left(\frac{1}{t}\right) \leq 1$$ Then $$-\sqrt{t} \leq \sqrt{t} \cos \left(\frac{1}{t}\right) \leq \sqrt{t}$$ and $$\lim _{t \rightarrow 0+}-\sqrt{t}=\lim _{t \rightarrow 0+} \sqrt{t}=0$$ Hence, by the Squeeze Theorem, we get $$\lim _{t \rightarrow 0+} \sqrt{t} \cos \left(\frac{1}{t}\right)=0$$
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