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Question Number 185245 by Mastermind last updated on 19/Jan/23
Show that f(z)=z^2  is uniformly  continous in the region ∣z∣<R  where 0<R<∞.      Help!
$$\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{z}\right)=\mathrm{z}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{uniformly} \\ $$$$\mathrm{continous}\:\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mid\mathrm{z}\mid<\mathrm{R} \\ $$$$\mathrm{where}\:\mathrm{0}<\mathrm{R}<\infty. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$
Commented by Frix last updated on 19/Jan/23
What does “uniformly continous” mean?  The answer to your question is easy once  you understood the definition.
$$\mathrm{What}\:\mathrm{does}\:“\mathrm{uniformly}\:\mathrm{continous}''\:\mathrm{mean}? \\ $$$$\mathrm{The}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{your}\:\mathrm{question}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{once} \\ $$$$\mathrm{you}\:\mathrm{understood}\:\mathrm{the}\:\mathrm{definition}. \\ $$
Answered by 123564 last updated on 20/Jan/23

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