5. Suppose that a function f: R → R is a uniform limit of a sequence of polynomials on R.Prove that f is a polynomial.Hint: Use the uniform Cauchy criterion for uniform convergence.

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Answered: 5. Suppose that a function f: R → R is…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 34E

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5. Suppose that a function f: R → R is a uniform limit of a sequence of polynomials on R. Prove that f is a polynomial. Hint: Use the uniform Cauchy criterion for uniform convergence.