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Existance of this sequence

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data
    If f: R->R is differentiable at c in R, show that:
    f'(c)=lim(n{f(c+1/n)-f(c)})

    Show by example that the existance of this sequence doesn't imply the existence of f'(c)

    3. The attempt at a solution
    I got the second part, with my example just being |x|, but i'm not sure about the first part.
     
  2. jcsd
  3. Nov 29, 2008 #2
    Re: differentiability

    I assume the limit is to be taken as n -> infinity. Do you know the standard definition of the derivative of f at c? Can you take the definition in your problem and somehow change it to match the standard definition?
     
  4. Nov 29, 2008 #3
    Re: differentiability

    Show the work you've done, and think about the sequential criterion for limits.
     
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