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: 26

Answer

$0$

Work Step by Step

\begin{align*} \lim _{t\rightarrow 0} \frac{\cos t-\cos^2t}{t } &=\lim _{t\rightarrow 0} \frac{(1-\cos t)\cos t}{t } \\ &=\lim _{t\rightarrow 0} \frac{1-\cos t}{t } \lim _{t\rightarrow 0} \cos t \\ &=0. \end{align*} Where we used the fact that $\lim _{t\rightarrow 0} \frac{1-\cos t}{t } =0.$
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