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Corollary 1.1.2 If PA and Pg are two arbitrary partitions of [a,b] then L(f, PR)

Corollary 1.1.2 If PA and Pg are two arbitrary partitions of [a,b] then L(f, PR)

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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Corollary 1.1.2 If PA and Pg are two arbitrary partitions of [a,b] then L(f, PR) <U(f,PA).
Transcribed Image Text:Corollary 1.1.2 If PA and Pg are two arbitrary partitions of [a,b] then L(f, PR) <U(f,PA).
Goal: the following steps will guide you to prove proposition 1.2.1: VP, P2 par titions of [a, b), we have L(f, P) <| f(r)dr < f(r)dr <U(f, P). 1.1 Using corollary 1.1.2, prove that sup L(f, P) < inf U (f, P). P. 1.2 Deduce proposi tion 1.2.1.
Transcribed Image Text:Goal: the following steps will guide you to prove proposition 1.2.1: VP, P2 par titions of [a, b), we have L(f, P) <| f(r)dr < f(r)dr <U(f, P). 1.1 Using corollary 1.1.2, prove that sup L(f, P) < inf U (f, P). P. 1.2 Deduce proposi tion 1.2.1.
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