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

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