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

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Answer 1 · 2015-09-25T01:55:12

Refer to 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
$lim_{x to infty} arctan(e^x)=lim_{t to infty} arctan(t)=\pi/2$ .

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