| Line 1: | Line 1: | ||
| − | Suppose that f(a)=g(a)=0 and that f and g are differentiable on an open interval <i>I</i> containing a. <br> | + | Suppose that <math>f(a)=g(a)=0</math> and that f and g are differentiable on an open interval <i>I</i> containing a. <br> |
Suppose also that <math>g'(x)\neq0</math> on <i>I</i> if <math>x\neq a</math>. <br> | Suppose also that <math>g'(x)\neq0</math> on <i>I</i> if <math>x\neq a</math>. <br> | ||
Then <br> | Then <br> | ||
Latest revision as of 12:50, 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)\neq0 $ on I if $ x\neq a $.
Then
$ \lim_{x \to\ a}\frac{f(x)}{g(x)}= \lim_{x \to\ a}\frac{f'(x)}{g'(x)} $,
if the limit on the right exists (or is $ \infty $ or -$ \infty $
).
This is Elizabeth's favorite theorem.
