University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.9 - Inverse Trigonometric Functions - Exercises - Page 181: 16


$-\displaystyle \frac{\pi}{2}$

Work Step by Step

$y=\tan^{-1}x$ is the number in $(-\pi/2, \pi/2)$ for which $\tan y=x.$ In $(-\pi/2, \pi/2)$, we want the angle (in radians) for which $\tan x\rightarrow+\infty$. This is $-\displaystyle \frac{\pi}{2}$. Alternatively (if in doubt), we can reach the same conclusion by observing the graph of $y=\tan^{-1}x$ (also written as $\arctan x$) when $ x\rightarrow-\infty$. See below.
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