21. Find the upper and lower sums of f with the given partition. (a) f: (0,4] → R, f(x) = 3 · 10,1) +5·11,2) – 8 · 1 2,4) = {0,0.1,0.9,1.4, 2, 2.5, 3.7, 4} (b) f:[0,4] →R, f(x) = 3 · 1 0,2) +5 ·11,3) – 8 · 1/2,4) P = {0,0.1,0.9,1.4,2, 2.5, 3.7,4}
21. Find the upper and lower sums of f with the given partition. (a) f: (0,4] → R, f(x) = 3 · 10,1) +5·11,2) – 8 · 1 2,4) = {0,0.1,0.9,1.4, 2, 2.5, 3.7, 4} (b) f:[0,4] →R, f(x) = 3 · 1 0,2) +5 ·11,3) – 8 · 1/2,4) P = {0,0.1,0.9,1.4,2, 2.5, 3.7,4}
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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![21. Find the upper and lower sums of f with the given
partition.
(a) f:[0,4] → R,
f(x) = 3 · 10,1) +5· 11,2) – 8 · 1/2,4)
|
P= {0,0.1,0.9,1.4, 2, 2.5, 3.7,4}
(b) f: [0,4] → R,
f(x) = 3 · 1[0,2) +5.11,3) – 8 · 1 12,4)
P = {0,0.1,0.9,1.4,2, 2.5, 3.7,4}
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fcda1d8-b8c1-4c08-bb90-f406bd02444f%2Fdaa1bd5a-6e19-459a-84ac-537e7ae5a2fd%2Fs8x71r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:21. Find the upper and lower sums of f with the given
partition.
(a) f:[0,4] → R,
f(x) = 3 · 10,1) +5· 11,2) – 8 · 1/2,4)
|
P= {0,0.1,0.9,1.4, 2, 2.5, 3.7,4}
(b) f: [0,4] → R,
f(x) = 3 · 1[0,2) +5.11,3) – 8 · 1 12,4)
P = {0,0.1,0.9,1.4,2, 2.5, 3.7,4}
%3D
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