Show that I¿(f) = 1, and conclude that f is integrable on
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
ONLY PART D
![such that Lp(g) >1-
might make answering this part easier.
(c) Prove that for every e > 0, there exists a partition P of [0, 1] such that Lp(f) >1-e.
Hint. Use part (b).
(d) Show that I(f) = 1, and conclude that f is integrable on [0, 1].
E =
2
- €. Do a similar proof for n = 3 and n = 4. Doing this](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a55184-59cb-4c2c-8e9a-b4f3831e5579%2F5ffc387e-f8d3-405b-9140-d80ce1a904ef%2F0f4lv7k_processed.png&w=3840&q=75)
Transcribed Image Text:such that Lp(g) >1-
might make answering this part easier.
(c) Prove that for every e > 0, there exists a partition P of [0, 1] such that Lp(f) >1-e.
Hint. Use part (b).
(d) Show that I(f) = 1, and conclude that f is integrable on [0, 1].
E =
2
- €. Do a similar proof for n = 3 and n = 4. Doing this
![1 1 1
2'3'4
(7) Let A =
:n e Z and n >1
Let
....
So
if æ ¢ A
if x € A
f(x) =
In this question we will prove that f is integrable on [0, 1].
(a) Prove that (S) = 1.
(b) Prove that for every positive integer n, and for every e > 0, there exists a partition P of
[0, 1] such that Lp(f) >1 - -
Note: this question involves two arbitrary values, namely, n and e. So you might want to first
pick a value for n, say n = 2, and show that for any e > 0, there exists a partition P of [0, 1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a55184-59cb-4c2c-8e9a-b4f3831e5579%2F5ffc387e-f8d3-405b-9140-d80ce1a904ef%2F06d8j1_processed.png&w=3840&q=75)
Transcribed Image Text:1 1 1
2'3'4
(7) Let A =
:n e Z and n >1
Let
....
So
if æ ¢ A
if x € A
f(x) =
In this question we will prove that f is integrable on [0, 1].
(a) Prove that (S) = 1.
(b) Prove that for every positive integer n, and for every e > 0, there exists a partition P of
[0, 1] such that Lp(f) >1 - -
Note: this question involves two arbitrary values, namely, n and e. So you might want to first
pick a value for n, say n = 2, and show that for any e > 0, there exists a partition P of [0, 1]
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