Find the limit as x approaches infinity of ##y=arctan(e^x)##?

To answer this question, you need to know that ##lim_{x to +infty} e^x=+infty## and ##lim_{x to +infty} arctan x=pi/2## from the stuy of ##e^x## (see ) and of ##arctan x## (see ).

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##.