MATH 350, Supplementary problems for Homework 6

1. Prove that  f: x → ax + b is uniformly continuous on ℝ.
2. Prove that   f: x → x³ is not uniformly continuous on [a,∞).
3. If f is uniformly continuous on [1,∞) prove that there is a constant C such that   |f(x)| ≤ C|x| for x∈[1,∞).