1. Let f : D → R be uniformly continuous on D and let k ∈ R. Prove that the function k f is uniformly continuous on D. 2. suppose that g (x) ≠ 0 for all x ∈ D. (a) Find an example to show that the...

1. Let f : D → R be uniformly continuous on D and let k ∈ R. Prove that the function k f is uniformly continuous on D.

2. suppose that g (x) ≠ 0 for all x ∈ D.

(a) Find an example to show that the function f/g need not be uniformly continuous on D.

(b) Prove that if D is compact, then f/g must be uniformly continuous on D.

3. Prove or give a counterexample: If f : A → B is uniformly continuous on A and g : B → C is uniformly continuous on B, then g o f : A → C is uniformly continuous on A