x if 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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riemannintegral
x if 1<x <2
4 – x if 2<x < 3
Q1. Let f : [1,3] → R is given by f(x) =
(a) Show that f(x) is bounded.
(b) Let P = {1, , 2, , 3} is a partition for [1, 3].
Determine the lower Reimann Sum L(P, f) and the upper
Riemann Sum U(p, f).
(c) Let P1 = {1, , 2, , 4,3} is another partition for [1,3].
What is the relation between the two partitions P and P?
Compare L(P, f), U (p, f), L(P1, f), U (p1, f).
Transcribed Image Text:x if 1<x <2 4 – x if 2<x < 3 Q1. Let f : [1,3] → R is given by f(x) = (a) Show that f(x) is bounded. (b) Let P = {1, , 2, , 3} is a partition for [1, 3]. Determine the lower Reimann Sum L(P, f) and the upper Riemann Sum U(p, f). (c) Let P1 = {1, , 2, , 4,3} is another partition for [1,3]. What is the relation between the two partitions P and P? Compare L(P, f), U (p, f), L(P1, f), U (p1, f).
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