Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.6 - Limits at Infinity; Horizontal Asymptotes - 2.6 Exercises: 35

Answer

$$\lim\limits_{x\to\infty}\arctan(e^x)=\frac{\pi}{2}$$

Work Step by Step

$$A=\lim\limits_{x\to\infty}\arctan(e^x)$$ Let $t=e^x$. As $x\to\infty$, $e^x$ approaches $\infty$. Therefore, $t\to\infty$.$$A=\lim\limits_{t\to\infty}\arctan(t)$$$$A=\frac{\pi}{2}$$ *NOTES TO REMEMBER: $\lim\limits_{x\to\infty}\arctan(x)=\frac{\pi}{2}$
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