Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises - Page 418: 30



Work Step by Step

Need to find the limit for $\lim\limits_{x \to (\frac{\pi}{2})^{+}}e^{tanx}$. Since, $tan(\frac{\pi}{2})^{+}=-\infty$ Thus, $\lim\limits_{x \to (\frac{\pi}{2})^{+}}e^{tanx}=e^{-\infty}=\frac{1}{e^{\infty}}$ Hence, $\lim\limits_{x \to (\frac{\pi}{2})^{+}}e^{tanx}=0$
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