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Math Help - Understanding formal statement of L'hospital's Rule

  1. #1
    Member roshanhero's Avatar
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    Understanding formal statement of L'hospital's Rule

    The Statement of L'hospital's Rule given on my book goes like this-
    "Let f and g be two real valued functions differentiable at each point x in (a-\delta,a+\delta),and g'(x) is not equal to 0 for all x such that <br />
0<\mid x-a\mid <\delta<br />
.
    If \lim_{x\rightarrow a} f'(x)/g'(x)exists and \lim_{x\rightarrow a} f(x)=0=\lim_{x\rightarrow a} g(x),then \lim_{x\rightarrow a} f(x)/g(x) also exists and \lim_{x\rightarrow a} f(x)/g(x)= \lim_{x\rightarrow a} f'(x)/g'(x)
    Last edited by roshanhero; April 12th 2009 at 10:53 PM. Reason: wrong syntax
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm trying to figure out what you're asking here....

    Quote Originally Posted by roshanhero View Post
    The Statement of L'hospital's Rule given on my book goes like this-
    "Let f and g be two real valued functions differentiable at each point x in (a-\delta ,a+\delta )and g'(x) is not equal to 0 for all x such that  0<\mid x-a\mid <\delta.
    If
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  3. #3
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  4. #4
    Member roshanhero's Avatar
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    I just could not understand the conditions given there for the L'hospital rule to apply i.e. the one given in the modulus sign.
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  5. #5
    MHF Contributor matheagle's Avatar
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    delta is small so that means for all x's near this a, but x does not equal a since we have the >0
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  6. #6
    Member roshanhero's Avatar
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    Can you post me the diagram so that I can visualise which will help me to understand the theory.
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