show that $\displaystyle \lim _ { z \to 0 } f(z) $ does not exist where :

$\displaystyle (1) f(z)= \frac {Re z}{z} : Z \neq 0 \downarrow

(2) 0 :z=0

$ by definition {i know how i solve it by CR equations }

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- Jul 15th 2009, 01:19 PMflower3please help me
show that $\displaystyle \lim _ { z \to 0 } f(z) $ does not exist where :

$\displaystyle (1) f(z)= \frac {Re z}{z} : Z \neq 0 \downarrow

(2) 0 :z=0

$ by definition {i know how i solve it by CR equations } - Jul 15th 2009, 01:40 PMPlato
$\displaystyle \frac{{\text{Re} (z)}}{z} = \frac{{x^2 - xyi}}{{x^2 + y^2 }}$

Now use polar substitution.