# L'Hopital's Rule.

#### SherlockOhms

1. Homework Statement

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

2. Homework Equations

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

3. 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.

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#### jbunniii

Homework Helper
Gold Member
1. Homework Statement

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

2. Homework Equations

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

3. 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!