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Proof of a limit involving definition of differentiability

  1. Apr 2, 2012 #1
    1. The problem statement, all variables and given/known data
    let the function f:ℝ→ℝ be differentiable at x=0. Prove that lim x→0
    [f(x2)-f(0)]
    ______________ =0
    x


    2. Relevant equations



    3. The attempt at a solution
    I am kind of lost on this one, I have tried manipulating the definition of a differentiable function at x=0 and I am not making much progress. I am not just looking for an answer here, this actually a review problem for a test and I am really trying to understand it so any help would be appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 2, 2012 #2

    Curious3141

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    Homework Helper

    Try L' Hopital's Rule.
     
  4. Apr 2, 2012 #3
    I am in an analysis class and we have not yet proved L' Hopital's Rule so I can not use it in this proof.
     
  5. Apr 2, 2012 #4

    Dick

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    Science Advisor
    Homework Helper

    Use the change of variable u=x^2. Now think about the limit as u->0.
     
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