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Epsilon-Delta Definition to prove the L'Hopital's Rule

  1. Oct 10, 2008 #1
    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
     
  2. jcsd
  3. Oct 11, 2008 #2
    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
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