Let f : [0, 1] → R be a function on the interval[0, 1]. Assume thatfor each polynomial p there is a point o in [0, 1] suchthat\f(xo) _p(æo)\ >1/2.Prove that the function f fails to be continuous onthe interval [0, 1].

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Answered: Let f [0, 1] → R be a function on the…

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 f [0, 1] → R be a function on the interval : [0, 1]. Assume that for each polynomial p there is a point o in [0, 1] such that f(xo) - p(xo) > 1/2. Prove that the function f fails to be continuous on the interval [0, 1].