Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.5 L'Hopital's Rule; Indeterminate Forms - Exercises Set 6.5: 8

Answer

=$\frac{2}{5}$

Work Step by Step

Since the limit as $x$ approaches zero is $\frac{0}{0}$, L'Hopital's Rule can be used. Taking the derivative of the numerator and denominator (using chain rule) yields $$\lim\limits_{x \to 0}\frac{2cos(2x)}{5cos(2x)}=\frac{2cos(0)}{5cos(0)}=\frac{2}{5}$$
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