Exercise 1. Recall that a function f: ER is called Lipschitz if there exists M such that |f(x) = f(y)| ≤ M|x - y| holds for all x, y ≤ E. i) Prove that if f: ER is Lipschitz, then f(x) is uniformly continuous. ii) Prove that f: [a, co) → R given by x√√x is Lipschitz on iii) Show f: [0, 0)→ R given by x√x is uniformly continuous, but not Lipschitz. [a, ∞o) for all a>0.

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