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Satisfies Cauchy-Riemann equations but not differentiable

  • Thread starter ak123456
  • Start date
  • #1
50
0

Homework Statement


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

Homework Equations





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 ?
 

Answers and Replies

  • #2
50
0
_z is x-iy
 
  • #3
200
0
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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