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
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 44PS: A company determines that its weekly profit from manufacturing and selling x units of a certain item...
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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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