limit as x approaches 0+ of x^(1/x)
The Attempt at a Solution
Usually I solve this limit by rewriting the limit as e^log(f(x)) and applying L'hopital rule. However:
(All limits approach 0+)
Lim x^(1/x) = exp( Lim log(x^(1/x)) ) = exp( Lim log(x) / x )
This is where I'd usually apply L'hopital rule and solve the problem. I can't tho, since x tends to 0 and log(x) tends to - infinity. I'm stuck here..
If anyone could point me in the right direction I'd appreciate.