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

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.