Let X be the set of all polynomials (of any degree) defined on [0, 1] and d(f, g) be the metric defined by d(f, g) = = sup f(x) = g(x)\. x= [0,1] (a) Prove that e* & X. (b) Prove that the sequence Pn(x) = (1 + ²)", n ≥ 1 is Cauchy but not convergent.

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