Given a function f : D → R defined on a set D, recall that the modulus of continuity is a function w(x0, 8) = sup{\f (x) – f(x0)| : x E D, x – xo| < 8}. Assume that f is uniform continuous on D. Prove that the function h(8) suproED W(x0, 8) satisfies: lim h(8) = 0. 8→0+

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