Question

What is the limit of `arctan(e^x)` as x goes to infinity?

Answer 1

Refer to explanation

Explanation:

We know that `lim_{x to +infty} e^x=+infty` and `lim_{x to +infty} arctan x=pi/2` from the stuy of `e^x` and of `arctan x`.

So, as `x to infty`, `e^x to infty` so that, letting `t=e^x` we have
`lim_{x to infty} arctan(e^x)=lim_{t to infty} arctan(t)=\pi/2`.