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    Real Analysis : Proof using an Integral and Mean Value Theorem

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    For numbers a1,....,an, define
    p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that:

    (a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0

    Prove that there is some point x in the interval (0,1) such that p(x) = 0

    © BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
    https://brainmass.com/math/integrals/real-analysis-proof-using-an-integral-and-mean-value-theorem-11672

    Solution Summary

    An integral and Mean Value Theorem are used to provide a real analysis proof.

    $2.49

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