Thread: L'Hospital's Rule problem

How would I use L'Hospital's Rule to evaluate the following limits? I don't know how to start these problems.

1. lim as x approaches infinity of xe^-sqrt x

2. lim as x approaches 0 of (xe^1/x-x)

$\displaystyle x\;e^{-\sqrt{x}}= \dfrac{x}{e^{\sqrt{x}}}$

as x -> infinity, the above has an indeterminate form...so take derivatives of the numerator and the denominator! if it still cant be determined, use lhopital's rule again!

q2: write your notation clearly.Learn LaTex. Also show your effort on the problem!