University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Practice Exercises - Page 111: 53

Answer

$$\lim_{x\to-\infty}\tan^{-1}x=-\frac{\pi}{2}$$
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Work Step by Step

$$A=\lim_{x\to-\infty}\tan^{-1}x$$ $y=\tan^{-1}x$ or $y=\arctan x$ is the inverse function of the tangent function. And as $x\to-\infty$, $\tan^{-1}x$ approaches $-\pi/2$. $$A=-\frac{\pi}{2}$$ A graph of the function $y=\tan^{-1}x$ has been included below for better visualization.
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