L'Hopital's Rule - Real Analysis | Lecture 27

In this lecture we state and prove three distinct versions of L'Hopital's rule. Each version deals with either a different indeterminate form for the quotient of functions or the limit being finite/infinite. We begin by proving Cauchy's Generalized Mean Value Theorem, which can be understood as an extension of the usual mean value theorem to parametric function curves. This variant of the mean value theorem is then used to prove the variants of L'Hopital's rule either directly or indirectly. Insightful examples and illustrations are provided to better motivate the results.

This course is taught by Jason Bramburger.