L'Hôpital's Rule at Infinity

L'Hôpital's Rule at Infinity

For limits as $$x\to\infty$$ or $$x\to-\infty$$, if the quotient gives $$\frac{0}{0}$$ or $$\frac{\infty}{\infty}$$:

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

when the required conditions are satisfied.

Usage

- Used for quotient limits at infinity that cannot be evaluated directly.