8. (a) Suppose f: [a, b] → R is integrable and L(f, P) = U(f, P) for some partition P of [a, b]. Whatcan we conclude about f?(b) Suppose f: [a, b] → R is integrable and L(f, P₁) = U(f, P₂) for some partitions P₁, P2 of [a, b].What can we conclude about f?(c) Suppose f: [a, b] → R is continuous with the property that L(f, P₁) = L(f, P₂) for all pairs ofpartitions P₁, P2 of [a, b]. What can we conclude about f?(d) Suppose f [a, b] → R is integrable with the property that L(f, P₁) = L(f, P₂) for all pairs ofpartitions P₁, P₂ of [a, b]. What can we conclude about f? You need not be completely rigorous.

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Answered: 8. (a) Suppose f : [a, b] → R is…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 70EQ

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8. (a) Suppose f : [a, b] → R is integrable and L(ƒ, P) = U(ƒ, P) for some partition P of [a, b]. What can we conclude about f?