# how to prove this function to be uniformly continuous ?

• March 13th 2011, 07:05 AM
PeaceSoul
how to prove this function to be uniformly continuous ?
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 ??
• March 13th 2011, 07:34 AM
girdav
$|z_1^5-z_2^5|=|z_1-z_2||z_1^4+z_1^3z_2+z_1^2z_2^2+z_1z_2^3+z_2^4|< 4|z_1-z_2|$ if $|z_1|<1$ and $|z_2|<1$
• March 13th 2011, 07:39 AM
PeaceSoul
first of all thank you for replyin. well is that it ? is that sufficient to prove that is uniformly continious?
• March 13th 2011, 07:56 AM
girdav
Yes, you can use the definition with $\varepsilon$ and $\delta$.