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

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Answer 1 · 2014-10-05T14:08:45

Let us figure this out from our knowledge about $tanx$ .

We know:

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

Since $arctan x$ is the inverse function of $tanx$ , $-pi/2 < x < pi/2$ , we can swapping the relationship above to obtain:

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

Hence,

$lim_{x to infty}arctanx=pi/2$ .

I hope that this was helpful.

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