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1) There is a continuous function from [1, 4] to R that is not uniformly continuous....

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Advance Math

1) There is a continuous function from [1, 4] to R that is notuniformly continuous. True or False and justify your answer.

2) Suppose f : D : ?R be a function that satisfies the followingcondition: There exists a real number C ? 0 such that |f(u) ? f(v)|? C|u ? v| for all u, v ? D. Prove that f is uniformly continuouson D

Definition of uniformly continuous: A function f: D?R is calleduniformly continuous iff for all sequences {an} and{bn} in D if (an) - (bn)? 0 thenf(an) - f(bn)? 0

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