4. Let C₁,..., Cn € [a, b] with c₁ < C₂ < ··· < Cn. E (a) Let f: [a, b] → R be a function such that f(x) = 0 for all x = [a, b] \ {c₁,..., Cn}. Prove [ºf that f is Riemann integrable on [a, b] and that Hint: Use question 3 and the generalization of assignment3, question 1, posted on my- Courses. (b) Let f : [a, b] → R and g [a, b] →→ R be functions such that f(x) = g(x) for all x € [a, b]\{c₁,..., cn}. Prove that if f is Riemann integrable on [a, b] then g is Riemann integrable on [a, b] and So = 0. f = g.
4. Let C₁,..., Cn € [a, b] with c₁ < C₂ < ··· < Cn. E (a) Let f: [a, b] → R be a function such that f(x) = 0 for all x = [a, b] \ {c₁,..., Cn}. Prove [ºf that f is Riemann integrable on [a, b] and that Hint: Use question 3 and the generalization of assignment3, question 1, posted on my- Courses. (b) Let f : [a, b] → R and g [a, b] →→ R be functions such that f(x) = g(x) for all x € [a, b]\{c₁,..., cn}. Prove that if f is Riemann integrable on [a, b] then g is Riemann integrable on [a, b] and So = 0. f = g.
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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Question
![4. Let C₁,..., Cn € [a, b] with c₁ < C₂ < · · · < En·
(a) Let f [a, b] → R be a function such that f(x) = 0 for all x = [a, b] \ {c₁,..., Cn}. Prove
L'of
that f is Riemann integrable on [a, b] and that
Hint: Use question and the generalization of assignment3, question 1, posted on my-
Courses.
f = 0.
(b) Let ƒ : [a, b] → R and g : [a, b] → R be functions such that f(x)
g(x) for all x €
[a, b]\{c₁,..., n}. Prove that if f is Riemann integrable on [a, b] then g is Riemann integrable
rb
¹ [₁ = ["²9.
on [a,b] and
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e52190b-50e6-4255-84a6-de0c6d0112f2%2F21c5f0f7-ae67-4ff0-b442-e6101f3af773%2Ff1vckvo_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let C₁,..., Cn € [a, b] with c₁ < C₂ < · · · < En·
(a) Let f [a, b] → R be a function such that f(x) = 0 for all x = [a, b] \ {c₁,..., Cn}. Prove
L'of
that f is Riemann integrable on [a, b] and that
Hint: Use question and the generalization of assignment3, question 1, posted on my-
Courses.
f = 0.
(b) Let ƒ : [a, b] → R and g : [a, b] → R be functions such that f(x)
g(x) for all x €
[a, b]\{c₁,..., n}. Prove that if f is Riemann integrable on [a, b] then g is Riemann integrable
rb
¹ [₁ = ["²9.
on [a,b] and
=
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