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

prasannaworld · Oct 10, 2008

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

robert Ihnot · Oct 11, 2008

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.

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

prasannaworld

robert Ihnot