L'Hopital's Rule: Evaluating Limits

[SherlockOhms]

Homework Statement

Use l'Hopital's rule to evaluate the following limit:
lim x→0 e^(-1/x) / x for x> 0.

Homework Equations

differentiate the top and bottom until a limit can be found. Possibly rewrite as a product.

The Attempt at a Solution

I was under the impression that l'Hopital's rule could only be used for evaluating limits of indeterminate form i.e. 0/0 or ∞/∞. The above quotient doesn't fall into this category, does it? If someone could clear this up for me it'd be great.

 

[jbunniii]

Homework Statement

Use l'Hopital's rule to evaluate the following limit:
lim x→0 e^(-1/x) / x for x> 0.

Homework Equations

differentiate the top and bottom until a limit can be found. Possibly rewrite as a product.

The Attempt at a Solution

I was under the impression that l'Hopital's rule could only be used for evaluating limits of indeterminate form i.e. 0/0 or ∞/∞. The above quotient doesn't fall into this category, does it? If someone could clear this up for me it'd be great.

What is $\lim_{x \to 0^+} e^{-1/x}$?

 

[SherlockOhms]

What is $\lim_{x \to 0^+} e^{-1/x}$?

It approaches some very small number. Ok, I see now. Thanks!