For the following functions ƒ on [0, 1], compute the upper and lower sums for the partition 1 Pn :0 < - < 2 <....< n п — 1 < 1, n and compute the limits lim L(f, Pn), lim U(f, Pn). Check your results using the Newton--Leibniz formula. n00 1. f(x)= x². 2. f(x) = x³. n(n+1)(2n+1) n°(n+1)? Hint: i? 6 4 i=1 i=1
For the following functions ƒ on [0, 1], compute the upper and lower sums for the partition 1 Pn :0 < - < 2 <....< n п — 1 < 1, n and compute the limits lim L(f, Pn), lim U(f, Pn). Check your results using the Newton--Leibniz formula. n00 1. f(x)= x². 2. f(x) = x³. n(n+1)(2n+1) n°(n+1)? Hint: i? 6 4 i=1 i=1
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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![For the following functions f on [0, 1], compute the upper and lower sums for the partition
1
Pn :0 <
2
く……く
n – 1
< 1,
n
n
and compute the limits lim L(f, Pn), lim U(f, Pn). Check your results using the Newton--Leibniz formula.
n00
n00
1. f(x) = x2.
2. f(x)= x³.
n
n(n+1)(2n+1)
n² (n+1)²
Hint: i?
6
4
i=1
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8c2ad84-3927-490a-bf66-2d9eb7f56b39%2Ff9acd6b4-347e-4e4e-94a0-5e4e39b1834d%2Fiaajryl_processed.png&w=3840&q=75)
Transcribed Image Text:For the following functions f on [0, 1], compute the upper and lower sums for the partition
1
Pn :0 <
2
く……く
n – 1
< 1,
n
n
and compute the limits lim L(f, Pn), lim U(f, Pn). Check your results using the Newton--Leibniz formula.
n00
n00
1. f(x) = x2.
2. f(x)= x³.
n
n(n+1)(2n+1)
n² (n+1)²
Hint: i?
6
4
i=1
i=1
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