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: 56



Work Step by Step

Given $$\lim _{x \rightarrow 0} \frac{12^{x}-1}{4^{x}-1}$$ Consider $$ f(x)= \frac{12^{x}-1}{4^{x}-1}$$ From the following figure, we can observe that \begin{align*} \lim _{\theta \rightarrow 0^+} f( x)&=1.8\\ \lim _{\theta \rightarrow 0^-} f( x)&=1.8 \end{align*} Then $$\lim _{x \rightarrow 0} \frac{12^{x}-1}{4^{x}-1}=1.8$$
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