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\displaystyle\lim_{x\to\a}\frac{f(x)}{g(x)}=\displaystyle\lim_{x\to\a}\frac{f'(x)}{g'(x)}
 
\displaystyle\lim_{x\to\a}\frac{f(x)}{g(x)}=\displaystyle\lim_{x\to\a}\frac{f'(x)}{g'(x)}
 
</math>,
 
</math>,
if the limis on the right exists (or is <math>infty</math>).
+
if the limis on the right exists (or is positive or negative infinity).
  
 
This is Elizabeth's favorite theorem.
 
This is Elizabeth's favorite theorem.

Revision as of 09:16, 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 $ \displaystyle\lim_{x\to\a}\frac{f(x)}{g(x)}=\displaystyle\lim_{x\to\a}\frac{f'(x)}{g'(x)} $, if the limis on the right exists (or is positive or negative infinity).

This is Elizabeth's favorite theorem.

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