Bernoulli-L'Hôpital's Rule

analysis calculus

Definition

L'Hospital's Rule

Let and be continuous on and differentiable on . Let such that:

If the limit of the ratio of their derivatives exists, then:

providing in a neighbourhood of .

Examples

The fraction results in an indeterminate form . Applying L’Hospital’s rule:

This results in . Applying the rule twice:

This results in the indeterminate form . Applying the rule times: