# GRE Subject Test: Math : L'Hospital's Rule

## Example Questions

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### Example Question #26 : L'hospital's Rule

Evaluate the following limit:

Explanation:

When we evaluate the limit using normal methods, we get the indeterminate form . When this happens, we must use L'Hopital's Rule, which states that

Now, we must find the derivatives of the numerator and denominator:

The derivatives were found using the following rules:

Next, rewrite the limit and evaluate it:

### Example Question #27 : L'hospital's Rule

Use l'Hopital's rule to find the limit:

Explanation:

The first thing we always have to do is to check that l'Hopital's rule is actually applicable when we want to use it.

So it is applicable here.

We take the derivative of the top and bottom, and get

and now we can safely plug in x=1 and get that the limit equals

.

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