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?
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?
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(f, P) = U(f, P) for some partition P of [a, b]. What
can 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 of
partitions 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 of
partitions P₁, P₂ of [a, b]. What can we conclude about f? You need not be completely rigorous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd22a7882-835a-44a8-b8af-d7a415b67cf6%2Fb1482e31-6237-40d4-863d-99b2625f878a%2Fatf8zkp_processed.png&w=3840&q=75)
Transcribed Image Text:8. (a) Suppose f: [a, b] → R is integrable and L(f, P) = U(f, P) for some partition P of [a, b]. What
can 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 of
partitions 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 of
partitions P₁, P₂ of [a, b]. What can we conclude about f? You need not be completely rigorous.
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