Trigonometry- Another limit function?

Question

What about Lim arctan(e^x) as x--> infinite

Explain too?? Thx (^_^)

Answer 1

As x approaches infinity, so also does e^x.

So your answer will be whatever happens to arctan(y) as y approaches infinity.  As y approaches infinity, arctan(y) approaches п/2.

So your answer is:

Lim arctan(e^x) = п/2 as x → ∞.