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 94: 32


$$\frac{4}{3} $$

Work Step by Step

We have $$ \lim _{x \rightarrow 0} \frac{ \sin4x }{\sin3x}=\lim _{x \rightarrow 0} \frac{4}{3}\frac{ \sin4x }{4x} \frac{ 3x }{\sin3x}\\ = \frac{4}{3}\lim _{4x \rightarrow 0}\frac{ \sin4x }{4x} \lim _{3x \rightarrow 0}\frac{ 3x }{\sin3x}= \frac{4}{3}. $$ Where we used, $\lim _{x\rightarrow 0}\frac{ \sin x}{ x}=1. $
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