Define the sequence of functions {fn(x)} on (0, 1] by { 2n²x; 2n (1 — пх); 2п 2n fn(x) = 0; (a) Sketch on the same axis the graphs of fı(x) to f5(x). (b) Find f(x)= lim fn(x) . (c) Evaluate o f(x)dx (d) Evaluate fo fn(x)dx (e) Evaluate lim | fn(x)dx (f) Under which condition(s) will lim fn(x)dx = | lim fn(x)dx?
Define the sequence of functions {fn(x)} on (0, 1] by { 2n²x; 2n (1 — пх); 2п 2n fn(x) = 0; (a) Sketch on the same axis the graphs of fı(x) to f5(x). (b) Find f(x)= lim fn(x) . (c) Evaluate o f(x)dx (d) Evaluate fo fn(x)dx (e) Evaluate lim | fn(x)dx (f) Under which condition(s) will lim fn(x)dx = | lim fn(x)dx?
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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b)only finding pointwise limit
![Define the sequence of functions {fn(x)} on [0, 1] by
2n2x;
2n(1 — па);
0;
x <
2n
fn(x)
2n
(a) Sketch on the same axis the graphs of f1(x) to f5(x).
(b) Find f(x) = lim fn(x) .
(c) Evaluate fo f(x)dx
(d) Evaluate fo fn(x)dx
1
(e) Evaluate lim
fn(x)dx
(f) Under which condition(s) will lim
| fn(x)dx
= /
lim fn(x)dx?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81422962-5677-4f69-a2a2-9456679be88a%2Ff6b19efd-e6ec-4482-adf5-4587f80d8e35%2Fo796jpa_processed.png&w=3840&q=75)
Transcribed Image Text:Define the sequence of functions {fn(x)} on [0, 1] by
2n2x;
2n(1 — па);
0;
x <
2n
fn(x)
2n
(a) Sketch on the same axis the graphs of f1(x) to f5(x).
(b) Find f(x) = lim fn(x) .
(c) Evaluate fo f(x)dx
(d) Evaluate fo fn(x)dx
1
(e) Evaluate lim
fn(x)dx
(f) Under which condition(s) will lim
| fn(x)dx
= /
lim fn(x)dx?
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