Advanced Calculus 1
Problem 1 If the function f : D → R is uniformly continuous andα is any number, show that the function αf : D → R also isuniformly continuous.
Problem2 Provethatiff:D→Randg:D→Rareuniformlycontinuousthensoisthe sum f + g : D → R.
Problem 3 Define f (x) = 2x + 1 for all x ∈ R. Prove that f isuniformly continuous.
Problem 4 Define f (x) = x3 + 1 for all x ∈ R. Prove that f isnot uniformly continuous.
