Limit X--->0

Hockeystar

1. The problem statement, all variables and given/known data

Limit X--->0 x^2/x

2. Relevant equations

L'hospitals rule. y=e^ln(y)

3. The attempt at a solution

I tried using the theory that works for limit x---> 0 x^x = 1. But I end up getting limit x---> 0 e^2/x = infinity. How should I set up l'hospitals law?

Dick

You don't need (and can't use) l'Hopital if the limit isn't indeterminant. If you look at ln(x^(2/x)) how does it behave?

Hockeystar

As x approaches 0+, ln(x) approaches negative infinity while 2/x approaches 0. I'm confused.

Dick

I would say as x->0+ 2/x approaches +infinity. (-infinity)*(+infinity) doesn't look indeterminant to me.

Hockeystar

Ah thanks I always mix up lim x to infinity and x to 0. So u get e^(-infinity) = 0

Dick

Right!