MarkSA

01-28-2008, 10:09 PM

Hello,

Find the limit as x -> infinity, of: arctan(e^x)

In this problem, i'm not entirely sure of the proper process to use to get the answer. If I just work with the inner part, I suppose I can say that as x approaches infinity, e^x approaches infinity. Then, would I just determine what arctan(x) does as x approaches infinity? Is there a way to determine this without a graphing calculator? I have the general idea what sin,cos,tan functions look like, but I have trouble picturing what the inverses would look like (reflected about the line y=x.) I know in this case the limit is pi/2, but i'm not sure how I would do other problems like this without a graphing calculator.

Find the limit as x -> infinity, of: arctan(e^x)

In this problem, i'm not entirely sure of the proper process to use to get the answer. If I just work with the inner part, I suppose I can say that as x approaches infinity, e^x approaches infinity. Then, would I just determine what arctan(x) does as x approaches infinity? Is there a way to determine this without a graphing calculator? I have the general idea what sin,cos,tan functions look like, but I have trouble picturing what the inverses would look like (reflected about the line y=x.) I know in this case the limit is pi/2, but i'm not sure how I would do other problems like this without a graphing calculator.