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Satisfies Cauchy-Riemann equations but not differentiable

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f denote the function defined by
    f(z)=
    _z^2 /z if z is not 0
    0 if z=0
    show that f satisfies the Cauchy-Riemann equations at z=0 but that f is not differentiable there

    2. Relevant equations



    3. The attempt at a solution
    it is easily to show the function satisfies Cauchy-Riemann equations
    but how to show it is not differentiable
    can i show f'(0) does not exist when z tends to 0 ?
     
  2. jcsd
  3. Apr 21, 2009 #2
    _z is x-iy
     
  4. Apr 21, 2009 #3
    What you need to show is that f'(0) = lim_{h -> 0} ((f(h) - f(0))/h = lim_{h -> 0} _h^2/h^2. does not exist. To show that this limit does not exist, try approaching 0 in two different ways and show you get something different.
     
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