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: 31



Work Step by Step

\begin{align*} \lim _{h\rightarrow 0} \frac{ \sin h}{5h}&=\lim _{h\rightarrow 0} \frac{1}{5} \frac{ \sin h}{ h} \\ &= \frac{1}{5} \lim _{h\rightarrow 0}\frac{ \sin h}{ h} \\ &= \frac{1}{5} . \end{align*} Where we used Theorem 2 -- that is, $\lim _{x\rightarrow 0}\frac{ \sin x}{ x}=1. $
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