- #1
ganondorf29
- 54
- 0
Homework Statement
Find the limit as x->0+ of (ln(x))^x
*The answer is 1*
Homework Equations
l'Hôpital's rule
The Attempt at a Solution
lim (ln(x))^x = 0^0
I took the ln of that quantity to bring down the x
lim = x*ln(ln(x))
lim = ln(ln(x)) / (1/x)
Then I used l'Hôpital's rule
1/(x*ln(x)/(1/x^2)
= 1/(x^3*ln(x))
I got stuck here. If I plug in zero I get 0^3 and a undefined answer in the denominator. Do I have to do l'Hôpital's rule on the bottom again?
Last edited: