Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.7 L'Hôpital's Rule - Exercises - Page 366: 9

Answer

$0$

Work Step by Step

Since we have $$ \lim _{x \rightarrow 0} \frac{\cos 2x-1}{\sin 5x }=\frac{0}{0} $$ then we can apply L’Hôpital’s Rule as follows $$ \lim _{x \rightarrow 0} \frac{-2\sin 2x}{5\cos 5x }=\frac{0}{5}=0. $$
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