Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 55: 57

Answer

$0.693$

Work Step by Step

Given $$\lim _{x \rightarrow 0} \frac{2^{x}-\cos x}{x}$$ Consider $$ f(x)= \frac{2^{x}-\cos x}{x}$$ From the following figure, we can observe that \begin{align*} \lim _{x\rightarrow 0^+} f( x)&=0.693\\ \lim _{x \rightarrow 0^-} f( x)&=0.693 \end{align*} Then $$\lim _{x \rightarrow 0} \frac{2^{x}-\cos x}{x}=0.693$$
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