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

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

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Answer 1 · 2014-10-05T14:08:45

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

We know:

as $x \to \frac{π}{2}^{-}$ $x to pi/2"^-$ , $tan x \to + \infty$ $tanx to +infty$

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

as $x \to + \infty$ $x to +infty$ , $arctan x \to \frac{π}{2}^{-}$ $arctanx to pi/2"^-$

Hence,

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

I hope that this was helpful.

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

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