Consider the function f(x) = √x+4 0 0 < x≤ ²/ 2 < x < 3 2 on the interval (0, 3). The Fourier sine series expansion of f(x) on (0, 3) has the form f(x) bn sin(npx), 0 < x < 3, (1) n=1 Denote by S(x) the sum of the Fourier sine series in (1) where x is any real number. (a) What is the value of p? (b) Enter the value of bn, n ≥ 1. (c) Evaluate S(¹).
Consider the function f(x) = √x+4 0 0 < x≤ ²/ 2 < x < 3 2 on the interval (0, 3). The Fourier sine series expansion of f(x) on (0, 3) has the form f(x) bn sin(npx), 0 < x < 3, (1) n=1 Denote by S(x) the sum of the Fourier sine series in (1) where x is any real number. (a) What is the value of p? (b) Enter the value of bn, n ≥ 1. (c) Evaluate S(¹).
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.3: Quadratic Functions
Problem 8CQ
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![Problem #3: Consider the function
Problem #3(a):
Problem #3(b):
Problem #3(c):
Problem #3(d):
f(x)
=
x+4 0<x< </2/2
0
< x < 3
on the interval (0, 3). The Fourier sine series expansion of f(x) on (0, 3) has the form
f(x) bn sin(npx), 0 < x < 3, (1)
n=1
Denote by S(x) the sum of the Fourier sine series in (1) where x is any real number.
(a) What is the value of p?
(b) Enter the value of bn, n ≥ 1.
(c) Evaluate S(¹).
(d) Evaluate S(-3).
Enter your answer symbolically,
as in these examples
Enter your answer as a symbolic
function of n, as in these
examples
Enter your answer symbolically,
as in these examples
Enter your answer symbolically,
as in these examples](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b416b9e-1151-42d9-91e6-c99f7088d177%2F1f2eac8e-0eb1-48b2-abbb-fabb344de349%2Fbj4gpt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem #3: Consider the function
Problem #3(a):
Problem #3(b):
Problem #3(c):
Problem #3(d):
f(x)
=
x+4 0<x< </2/2
0
< x < 3
on the interval (0, 3). The Fourier sine series expansion of f(x) on (0, 3) has the form
f(x) bn sin(npx), 0 < x < 3, (1)
n=1
Denote by S(x) the sum of the Fourier sine series in (1) where x is any real number.
(a) What is the value of p?
(b) Enter the value of bn, n ≥ 1.
(c) Evaluate S(¹).
(d) Evaluate S(-3).
Enter your answer symbolically,
as in these examples
Enter your answer as a symbolic
function of n, as in these
examples
Enter your answer symbolically,
as in these examples
Enter your answer symbolically,
as in these examples
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