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
$$
\lim _{x \rightarrow 0} \frac{-2\sin 2x}{5\cos 5x }=\frac{0}{5}=0.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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