Prove directly from the definition of uniform continuity that is uniformly continuous on

(Hint: a unit circle may help to make an estimation.)

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- October 25th 2009, 07:36 PMcgiulzprove sin(x) is uniformly continuous.
Prove directly from the definition of uniform continuity that is uniformly continuous on

(Hint: a unit circle may help to make an estimation.) - October 25th 2009, 08:01 PMKrizalid
prove that holds for and you're done.

- October 25th 2009, 09:45 PMcgiulz
Anything wrong with this argument?

given

- October 25th 2009, 09:49 PMBruno J.
Double post.

- October 25th 2009, 09:51 PMBruno J.

is wrong. Take m=0, n=1 for example. - October 25th 2009, 09:53 PMcgiulz
- October 25th 2009, 09:55 PMJose27
Since the derivative is bounded, using the mean value theorem you get that the function is uniformly continous.

- October 25th 2009, 10:04 PMredsoxfan325
- October 25th 2009, 10:06 PMcgiulz
- October 25th 2009, 10:07 PMredsoxfan325
- October 25th 2009, 10:11 PMcgiulz
- October 25th 2009, 10:16 PMredsoxfan325
- October 25th 2009, 10:22 PMJose27
You could say that is unif. cont. in and since it's periodic it's unif. cont. in

Edit. Apparently I keep avoiding the definition of uniform cont. - October 25th 2009, 10:32 PMcgiulz
- October 25th 2009, 10:34 PMredsoxfan325
That is true, yes, but I think you need to show that , not just state it.