section 5.9 solutions

A if f x 0 on a b then f is nondecreasing on a b

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Unformatted text preview: . a If f (x) ≥ 0 on [a, b], then F is nondecreasing on [a, b] and F (b) − F (a) ≥ 0. If f (x) > 0 on [a, b], then F is increasing on [a, b] and F (b) − F (a) > 0. 31. Since m ≤ f (x) ≤ M for all x ∈ [a, b], it follows from (5.8.3) that b b m dx ≤ a 33. b f (x) dx ≤ 2x a and so m(b − a) ≤ x dt √ =x 1+ t x 3 −4 2x dt √ 1+ t M dx a b x 3 −4 H (x ) = H (x ) = x f (x) dx ≤ M (b − a) a H (2) = 2 3x 2 2 − + √ √ 1 + 2x 1 + x3 − 4 12 2 − + 3 3 4 4 x 3 −4 2x dt ...
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This document was uploaded on 11/11/2013.

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