L'Hôpital's Rule

L'Hôpital's Rule

If:

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

gives an indeterminate form $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$, and the required conditions are satisfied, then:

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

provided the limit on the right exists.

Usage

- Used to evaluate difficult quotient limits producing $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$.