Limit involving natural log

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

nicksauce

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

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.

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.

fk378

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

Saladsamurai

Well then, what are the special cases in which L'Hopital's Rule can be applied? That is what are indeterminate forms?

Casey