L'Hopital's Rule
Read this section to learn how to use and apply L'Hopital's Rule. Work through practice problems 1-3.
Strong Version of L'Hôpital's Rule
L'Hô pital's Rule can be strengthened to include the case when and the indeterminate form " ", the case when both and increase without any bound.
L'Hô pital's Rule (Strong " " and " " forms)
If and are differentiable on an open interval which contains the point a, on I except possibly at , and
then provided the limit on the right exists.
( " " can represent a finite number or " ". )
Solution: As " ", both and increase without bound so we have an " " indeterminate form and can use the Strong Version l'Hô pital's Rule:
The limit of may also be an indeterminate form, and then we can apply l'Hô pital's Rule to the ratio . We can continue using l'Hô pital's Rule at each stage as long as we have an indeterminate quotient.