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    Analysis Proof Absolute Value

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    Say abs = absolute value.
    Suppose that the function f:[a,b]->R is Lipschitz;
    that is , there is a number c such that:

    abs(f(u) - f(v)) <= (c)abs(u-v)

    for all u and v in [a,b]. Let P be a partition of [a,b] and R(f,P) be a Riemann sum based on P. Prove that

    abs((R(f,P)) - (the integral from a to b of f)) <= ||P||(b-a)

    © BrainMass Inc. brainmass.com March 6, 2023, 1:16 pm ad1c9bdddf

    Solution Preview

    Please see the attachement.
    <br>I am not very clear of ||P||.

    Proof: Since ...

    Solution Summary

    An analysis proof for an absolute value is found. The partition of a Riemann sum based on a function is given.