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.