Solve Exponential Limit Problem

[planauts]

Hi, I am having trouble with this exponential limit problem.

Homework Statement

\lim \ x \rightarrow 0 \ [ e^{-1/x}]

Homework Equations

Answer: 0

The Attempt at a Solution

\lim x \rightarrow 0 e^(-x)^{-1}
\lim x \rightarrow 0 e^{-1}^{x}^{-1}
I don't think the second step is right. When i did that I ended up getting 1, which is incorrect.

Thanks for your help!

EDIT: @Mentallic I fixed it, thanks.

 

[Mentallic]

Umm.. could you try fixing up your latex please. If you need a few characters to be exponentiated, type it as so: a^{bc}=a^{bc} while a^bc=a^bc so just replace your brackets with the curly brackets.

 

[Gib Z]

The limit does not exist. Check what the expression approaches from the left and from the right separately.