# 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)

Â© BrainMass Inc. brainmass.com March 6, 2023, 1:16 pm ad1c9bdddfhttps://brainmass.com/math/integrals/analysis-proof-absolute-value-11674

#### 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.

$2.49