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

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

71
Jul 24, 2014

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 Exponential functions ) and of #arctan x# (see inverse cosine and inverse tangent ).

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#.

Was this helpful? Let the contributor know!
1500
Impact of this question
36022 views around the world
You can reuse this answer
Creative Commons License