| Line 3: | Line 3: | ||
\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)}= \lim_{x \to\ a}\frac{f'(x)}{g'(x)} | ||
</math>, <br> | </math>, <br> | ||
| − | if the limis on the right exists (or is | + | if the limis on the right exists (or is <math>\infty</math> or -<math>\infty</math> |
| + | ). | ||
This is Elizabeth's favorite theorem. | This is Elizabeth's favorite theorem. | ||
Revision as of 11:43, 4 September 2008
Suppose that f(a)=g(a)=0 and that f and g are differentiable on an open interval I containing a. Suppose also that g'(x)/=0 on I if x/=a. Then
$ \lim_{x \to\ a}\frac{f(x)}{g(x)}= \lim_{x \to\ a}\frac{f'(x)}{g'(x)} $,
if the limis on the right exists (or is $ \infty $ or -$ \infty $
).
This is Elizabeth's favorite theorem.
