(Review of Chapter 7 PMA) Find a sequence {fn} of continuous functions on [0, 1] such that: (a) fn(x) → 0, point-wise on [0, 1], | [₁ fn (2) dx | < S fn (x) dx < M < ∞, for all n € N, for a positive constant M. 1 (b) (c) lim n→∞ fn(x) dx = 1 0 dx = 0.
(Review of Chapter 7 PMA) Find a sequence {fn} of continuous functions on [0, 1] such that: (a) fn(x) → 0, point-wise on [0, 1], | [₁ fn (2) dx | < S fn (x) dx < M < ∞, for all n € N, for a positive constant M. 1 (b) (c) lim n→∞ fn(x) dx = 1 0 dx = 0.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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![(Review of Chapter 7 PMA) Find a sequence {fn} of continuous functions on [0, 1]
such that:
(a) fn(x) → 0, point-wise on [0, 1],
•1
(b) | S
|f₁ fn(1) dx |
(c) lim √ √ ²
S
∙1
N→∞
0
Do we contradict the conclusion of the "passing to the limit under integral" Theorem
fn(x) dx < M < ∞, for all n Є N, for a positive constant M.
fn (x) dx ‡
=
1
l'
0 dx = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2F56ed9a2e-e533-49b5-ace1-f20e4f6462e3%2F210pcbo_processed.png&w=3840&q=75)
Transcribed Image Text:(Review of Chapter 7 PMA) Find a sequence {fn} of continuous functions on [0, 1]
such that:
(a) fn(x) → 0, point-wise on [0, 1],
•1
(b) | S
|f₁ fn(1) dx |
(c) lim √ √ ²
S
∙1
N→∞
0
Do we contradict the conclusion of the "passing to the limit under integral" Theorem
fn(x) dx < M < ∞, for all n Є N, for a positive constant M.
fn (x) dx ‡
=
1
l'
0 dx = 0.
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