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: 53


$$- \frac{9}{2}.$$

Work Step by Step

\begin{align*} \lim _{h \rightarrow 0}\frac{\cos 3 h-1}{h^2}&= \lim _{h \rightarrow 0}9 \frac{\cos 3 h-1}{(3h)^2}\\ &= - 9\lim _{3h \rightarrow 0} \frac{1-\cos 3 h}{(3h)^2}\\ &=- \frac{9}{2}.\\ \end{align*} Where we used the fact that $\lim _{h \rightarrow 0} \frac{1-\cos h}{h^2}=\frac{1}{2}$.
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