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

Answer 1

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.

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Answer 2

Charles Anctil

The limit as x approaches infinity of arctan(x) is π/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.