Repeated Application of L'Hôpital's Rule

Repeated Application of L'Hôpital's Rule

If applying L'Hôpital's rule once still produces an indeterminate form, it can be applied again:

$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}=\lim_{x\to a}\frac{f''(x)}{g''(x)}$$

provided every application satisfies the required conditions.

Usage

- Used when multiple differentiations are necessary to evaluate a limit.