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Thread: how to prove this function to be uniformly continuous ?

  1. #1
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    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 ??
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  2. #2
    Super Member girdav's Avatar
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    $\displaystyle |z_1^5-z_2^5|=|z_1-z_2||z_1^4+z_1^3z_2+z_1^2z_2^2+z_1z_2^3+z_2^4|< 4|z_1-z_2|$ if $\displaystyle |z_1|<1$ and $\displaystyle |z_2|<1$
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  3. #3
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    first of all thank you for replyin. well is that it ? is that sufficient to prove that is uniformly continious?
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  4. #4
    Super Member girdav's Avatar
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    Yes, you can use the definition with $\displaystyle \varepsilon$ and $\displaystyle \delta$.
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