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

↳Redirected from "Find the limit as x approaches infinity of #xsin(1/x)#?"

1 Answer

Konstantinos Michailidis

Sep 25, 2015

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#.

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