L'Hôpital's Rule
Under the stated differentiability and continuity conditions, if and , then when the latter limit exists.
Theorem 1.14 (L'Hôpital's Rule)
Let and be differentiable at with continuous first derivatives there, and
then if ,
provided that the limit on the RHS exists.
Proof
By Taylor’s theorem,
and
as . Since and ,
Related
Stated in
- Theorem 1.14 (L'Hôpital's Rule)§1.5 L’Hôpital’s Rule