# Infinitely Differentiable Function that's not Analytic

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com May 24, 2023, 1:04 pm ad1c9bdddfhttps://brainmass.com/math/integrals/infinitely-differentiable-function-not-analytic-11036

#### Solution Summary

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

$2.49