Limit involving natural log

1. Dec 20, 2007

fk378

1. The problem statement, all variables and given/known data
Find the limit of (tanx)^cosx as x-->infinity
Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity)

3. The attempt at a solution
I did ln(tanx)^cosx = cosxlntanx
I know the limit of tanx as x-->infinity is pi/2
the limit of cosx as x-->infinity is infinity

Now, I don't know where to go from here

Last edited: Dec 20, 2007
2. Dec 20, 2007

nicksauce

"the limit of cosx as x-->infinity is 1 (or is it infinity?)"
That limit doesn't exist.

3. Dec 20, 2007

fk378

Oh okay. So now I have infinity x infinity. I can use L'Hopital's rule but I don't know how to set up the function.

4. Dec 20, 2007

HallsofIvy

No, you cannot use L'Hopital's rule for that. "Infinity* infinity" is not one of cases for which you can use L'Hopital's rule- nor do you need to. You have already been told the answer.

5. Dec 20, 2007

fk378

I just noticed in the directions it says to rearrange the problem so that you can use L'Hopital's rule.

6. Dec 20, 2007