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Prove that there exists real number p - ILL 1990 SWE4

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September 19, 2010
functiontrigonometryalgebra unsolvedalgebra

Problem Statement

Given function f(x)=sin⁡x+sin⁡πxf(x) = \sin x + \sin \pi x and positive number dd. Prove that there exists real number pp such that ∣f(x+p)−f(x)∣<d|f(x + p) - f(x)| < d holds for all real numbers xx, and the value of pp can be arbitrarily large.
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