L'Hôpital's Rule
Revision as of 16:06, 29 March 2009 by Boy Soprano II (talk | contribs) (L'Hopital's Rule moved to L'Hôpital's Rule: It should be l'Hôpital or l'Hospital)
L'Hopital's Rule is a theorem dealing with limits that is very important to calculus.
Theorem
The theorem states that for real functions 
, if 
![\[\lim\frac{f(x)}{g(x)}=\lim\frac{f'(x)}{g'(x)}\]](http://latex.artofproblemsolving.com/6/7/6/67664051ac365e271260749b981666330b2b71af.png)
Note that this implies that ![\[\lim\frac{f(x)}{g(x)}=\lim\frac{f^{(n)}(x)}{g^{(n)}(x)}=\lim\frac{f^{(-n)}(x)}{g^{(-n)}(x)}\]](http://latex.artofproblemsolving.com/f/6/6/f66ad9bb5b49e51afc1bf4dac34285dae981fd6f.png)
Proof
- No proof of this theorem is available at this time. You can help AoPSWiki by adding it.
Problems
Introductory
- Evaluate the limit
(<url>weblog_entry.php?t=168186 Source</url>)
(<url>weblog_entry.php?t=168186 Source</url>)
