how to prove this function to be uniformly continuous ?

**PeaceSoul** · March 13th 2011, 07:05 AM

i have a problem that i am not able to solve and i was hoping you could please help me!

let f be the function defined in the region |z| < 1, by f(z) = z^5 . prove that f is uniformly continious in |z| <1 ..how can i do this :S ??

**girdav** · March 13th 2011, 07:34 AM

$|z_1^5-z_2^5|=|z_1-z_2||z_1^4+z_1^3z_2+z_1^2z_2^2+z_1z_2^3+z_2^4|< 4|z_1-z_2|$ if $|z_1|<1$ and $|z_2|<1$

**PeaceSoul** · March 13th 2011, 07:39 AM

first of all thank you for replyin. well is that it ? is that sufficient to prove that is uniformly continious?

**girdav** · March 13th 2011, 07:56 AM

Yes, you can use the definition with $\varepsilon$ and $\delta$ .

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