L'Hôpital's rule helps us find limits in the form x→climv(x)u(x) where direct substitution ends in the indeterminate forms 00 or ∞∞.
The rule essentially says that if the limit x→climv′(x)u′(x)exists, then the two limits are equal:
The AP Calculus course doesn't require knowing the proof of this fact, but we believe that as long as a proof is accessible, there's always something to learn from it. In general, it's always good to require some kind of proof or justification for the theorems you learn.
Using L’Hôpital’s rule for finding limits of indeterminate forms