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    Infinitely Differentiable Function that's not Analytic

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    Use the given information:

    the functions g:[a,b]->R and h:[a,b]->R are continuous with h(x) >= 0 for all x in [a,b], and there is a point c in (a,b) such that:

    the integral from a to b of h(x)g(x)dx =
    g(c) times the integral from a to b of h(x)dx.

    to show that the Cauchy Integral Remainder Theorem implies the Lagrange Remainder Theorem if the function f^(n+1):I->R is assumed to be continuous.

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    Solution Summary

    Integral relations are used to prove the continuity of a given function in this solution.