L'Hôpital's rule is a method of solving limits of or with derivatives. Other limits of indeterminate form can be manipulated into either of those and then solved using L'Hôpital's rule.

Requirements

Given the following limit

L'Hôpital's rule requires that

and must be continuous and differentiable on an interval around but not including .
on the same interval as requirement #1
and must both tend towards or both tend towards

Definition

If all the requirements for L'Hôpital's rule as satisfied then

alternatively written using Lagrange's notation

Example

Given the function what is the limit as approaches ?

Note

Notice how L'Hôpital's rule was applied multiple times as the limit was still indeterminate after it was applied the first 2 times.