Answer
$$\lim_{x\to-\infty}\tan^{-1}x=-\frac{\pi}{2}$$
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.
