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: 32



Work Step by Step

\begin{align*} \lim _{x\rightarrow \frac{\pi}{6}} \frac{ x}{\sin 3x}&= \frac{ \pi/6}{\sin 3\pi/6} \\ &= \frac{ \pi/6}{\sin (3\pi/6)} \\ &= \frac{ \pi/6}{\sin (\pi/2)}\\ &= \frac{\pi}{6}. \end{align*} Where we used Theorem 2 -- that is, $\lim _{x\rightarrow 0}\frac{ \sin x}{ x}=1. $
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