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Advanced Calculus 1 Problem 1 If the function f : D → R is uniformly continuous...

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Advance Math

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.

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