Assume that f is continuous on [a, b] and let A be the area function for f

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Assume that f is continuous on [a, b] and let A be the area function for f with left endpoint a. Let m* and M* be the absolute minimum and maximum values of f on [a, b], respectively.

a. Prove that m*(x - a) ≤ A(x) ≤ M(x - a) for all x in [a, b]. Use this result and the Squeeze Theorem to show that A is continuous from the right at x = a.

b. Prove that m*(b - x) ≤ A(b) - A(x) ≤ M*(b - x) for all x in [a, b]. Use this result to show that A is continuous from the left at x = b.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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