## University Calculus: Early Transcendentals (3rd Edition)

$-\displaystyle \frac{\pi}{2}$
$y=\tan^{-1}x$ 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.