Real Analysis problem! Proving x^2 is continuous but NOT uniformly continuous on (inf, inf)

0:00 x^2 is continuous but NOT uniformly continuous on (inf, inf) but but is uniformly continuous on [a, b]
2:33 A useful theorem for showing NOT uniformly continuous
4:25 definition of f being continuous
5:58 definition of f being UNIFORMLY continuous
7:58 definition of f being NOT uniformly continuous
9:54 proving x^2 is uniformly continuous on [0, 1]
15:10 proving x^2 is NOT uniformly continuous on (inf, inf)
25:11 drawing that box!

Additional questions: Give an example of the following
Q1. f so that f(x) goes to inf as x goes to inf and f is uniformly continuous
Q2. f so that f(x) doesn't go to inf as x goes to inf and f is uniformly continuous
Q3. f so that f'(x) doesn't go to inf as x goes to inf and f is uniformly continuous
Q4. f so that f'(x) doesn't go to inf as x goes to inf and f is NOT uniformly continuous

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