What is the limit as x approaches infinity of arctan(x)?

Oct 5, 2014

Let us figure this out from our knowledge about $\tan x$.

We know:

as x to pi/2"^-, $\tan x \to + \infty$

Since $\arctan x$ is the inverse function of $\tan x$, $- \frac{\pi}{2} < x < \frac{\pi}{2}$, we can swapping the relationship above to obtain:

as $x \to + \infty$, arctanx to pi/2"^-

Hence,

${\lim}_{x \to \infty} \arctan x = \frac{\pi}{2}$.

I hope that this was helpful.