1. Using Definition 3.35, prove that each of the following functions is uniformly continuous on (0,1). (a)...

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1. Using Definition 3.35, prove that each of the following functions is uniformly continuous on (0,1).

(a) f(x) = x3 .

(b) f(x) = x2 - x.

(c) f(x) = x sin 2x.

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