Limit X Approaching 0: Solving Using L'Hospital's Rule and Exponential Functions

[Hockeystar]

Limit X--->0

Homework Statement

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

Homework Equations

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

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]

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

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]

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

Right!