Need clarification on a limit problem: lim_{x->infinity} arctan(e^x)

Dear Admin

Kindly delete this post. I found the answer. Sorry for the inconvenience.

Regards
 
Why delete it? It may be of interest to others.

I would say that the "solution" you found simply states the intuitive thinking. It is not technically valid, as you say, because infinity is not a number, and the theorem you refer to does not apply in this case.

What answer did you find? Did you find a similar theorem that applies to infinity?
 
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I found a similar problem with solution in James Stewart
 
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