1. Oct 10, 2008 #1

   prasannaworld

   

   Okay I wish to try to construct an Epsilon-Delta Definition to prove the L'Hopital's Rule (0/0 form). Please correct me if I am wrong.
   
   http://mathforum.org/library/drmath/view/53340.html
   
   I found the above site. Scrolling down one would the proof.
   
   I can follow how an x constraint is constructed. But then for the y constraint, I cannot seem to completely follow the proof when it says:
   
   lim f'(x0)/g'(x0) = L
   x0->b-
   
   Any help/guidance will be appreciated

    

   prasannaworld, Oct 10, 2008
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3. Oct 11, 2008 #2

   robert Ihnot

   

   Re: L'Hopital
   
   For a continuous function [tex]limF(x)_{x\rightarrow a}=F(a) [/tex]. In the use of L'Hopital's Rule, we can assume continuity because we are able to employ derivatives.
   
   So that, in general for continuous functions, we can see that [tex]lim\frac{F(x)}{G(x)}_{x\rightarrow a}=\frac{F(a)}{G(a)}[/tex] However, in the case of 0/0, we have an underfined quality and need to go further with it, as shown in your reference.

    

   Last edited: Oct 11, 2008

   robert Ihnot, Oct 11, 2008

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