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

Let X be the set of all polynomial (of any degree) defined on [0,1] and d (fig) be the metric…

Answered: Let X be the set of all polynomials (of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.