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Consider a bounded function f [a, b] → R and a partition P = U(f, P) ≥ U(f, Q) and L(f, P) ≤ L(f, Q). PROPOSITION of [a, b]. If Q is a refinement of P, then {xo, x1, x2,..., Xn}

Consider a bounded function f [a, b] → R and a partition P = U(f, P) ≥ U(f, Q) and L(f, P) ≤ L(f, Q). PROPOSITION of [a, b]. If Q is a refinement of P, then {xo, x1, x2,..., Xn}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please simply prove the lower sum version of the attached propositon

Consider a bounded function f [a, b] : U (ƒ, P) ≥ U (ƒ,Q) and PROPOSITION of [a, b]. If Q is a refinement of P, then → R and a partition P = L(f, P) ≤ L(ƒ, Q). {xo, x1, x2,..., n}
Transcribed Image Text:Consider a bounded function f [a, b] : U (ƒ, P) ≥ U (ƒ,Q) and PROPOSITION of [a, b]. If Q is a refinement of P, then → R and a partition P = L(f, P) ≤ L(ƒ, Q). {xo, x1, x2,..., n}
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