(5) Prove that Lp(f)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 34E
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![(5) Prove that Lp(f)<Uq(f) for any bounded function f and partitions P,Q of [a, b).
(Hint: Consider a common refinement R of P, Q.)
(6) Prove that Lp(f+g) > Lp(f)+Lp(g) for any bounded functions f, g and partition P of [a, b].
| 2021
(7) Let f(x) =
if x E Q
and a < b.
-2021
if æ ¢ Q.
(a) Let P = {a= x0,x1, · , Xn
b} be any partition of [a, b]. Find Lp(f) and Up(f).
%3D
(b) Prove that f is not integrable on the interval [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0feea5b0-6beb-4a66-a35c-f67ab69f7611%2F744b046d-1b7d-4196-abf7-ac15caf6b2a2%2Fcdwg0vq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(5) Prove that Lp(f)<Uq(f) for any bounded function f and partitions P,Q of [a, b).
(Hint: Consider a common refinement R of P, Q.)
(6) Prove that Lp(f+g) > Lp(f)+Lp(g) for any bounded functions f, g and partition P of [a, b].
| 2021
(7) Let f(x) =
if x E Q
and a < b.
-2021
if æ ¢ Q.
(a) Let P = {a= x0,x1, · , Xn
b} be any partition of [a, b]. Find Lp(f) and Up(f).
%3D
(b) Prove that f is not integrable on the interval [a, b].
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