1. Let f : D → Mark each statement True or False. Justify each answer. (a) In the definition of uniform continuity, the positive δ depends only on the function f and the given ε > 0. (b) If f is...

1. Let f : D →

Mark each statement True or False. Justify each answer.

(a) In the definition of uniform continuity, the positive δ depends only on the function f and the given ε > 0.

(b) If f is continuous and (x n) is a Cauchy sequence in D, then ( f (x n )) is a Cauchy sequence.

(c) If f : (a, b) → R can be extended to a function that is continuous on [a, b ], then f is uniformly continuous on (a, b).

2. Let f and g be real-valued functions that are uniformly continuous on D. Prove that f + g is uniformly continuous on D.