# Use L'Hopital's Rule to evaluate the limit

by Shay10825
Tags: evaluate, lhopital, limit, rule
 HW Helper P: 1,021 Well, what you have here is a case of f(x)^g(x) which yields the indeterminate form $\infty ^0$. You can convert it to another indeterminate form by doing $\exp \left( {\ln \left( {f\left( x \right)^{g\left( x \right)} } \right)} \right) = \exp \left( {g\left( x \right)\ln \left( {f\left( x \right)} \right)} \right)$. Then you have something of the form f(x)g(x) which gives a new indeterminate form $\infty \cdot 0$. Finally, you can convert this to f(x)/(1/g(x)) (or the other way arround) to get either 0/0 or inf/inf so that you can use L'Hopital.