Is uniformly continuous on ? Justify your answer.
(Note: It's slope at 0 is infinite)
Consider this
Continuous function - Wikipedia, the free encyclopedia
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.