Is uniformly continuous on ? Justify your answer.

(Note: It's slope at 0 is infinite)

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- Oct 25th 2009, 07:39 PMcgiulzIs the sqrt(x) uniformly continuous on [0,inf)?
Is uniformly continuous on ? Justify your answer.

(Note: It's slope at 0 is infinite) - Oct 25th 2009, 07:56 PMpickslides
Consider this

Continuous function - Wikipedia, the free encyclopedia - Oct 25th 2009, 08:00 PMKrizalid
yes, it is.

let's break that set into

note that the first set is compact, so is automatically uniformly continuous there, but as for the second set, for each is and this satisfies Lipschitz condition, hence we have uniform continuity on the second set, and finally on the whole set. - Oct 25th 2009, 08:09 PMrn443