(c) By evaluating the Fourier series for appropriate values of x, find the following sums: (-1)"+1 n² + 1 (i) X= - Σ n=1 1 n² + 1 and (ii) Y = Σ Y= n=1 (d) Find the corresponding Fourier coefficients in the Fourier series for y(x), which is periodic and satisfies the differential equation d²y - y = f(x). dx²
(c) By evaluating the Fourier series for appropriate values of x, find the following sums: (-1)"+1 n² + 1 (i) X= - Σ n=1 1 n² + 1 and (ii) Y = Σ Y= n=1 (d) Find the corresponding Fourier coefficients in the Fourier series for y(x), which is periodic and satisfies the differential equation d²y - y = f(x). dx²
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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
Related questions
Question
![3. Let the function f be defined by
for - < x < π and satisfy
f(x+2) = f(x).
Recall that cosh x = (e* + e*)/2 and in the following you are given the indefinite integral
So
1
a² + b²
for constants a and b.
cosh(ax) cos(bx)dx=
f(x) = cosh x
∞
(i) x = Σ
X
n=1
(c) By evaluating the Fourier series for appropriate values of x, find the following sums:
(a sinh(ax) cos(bx) + b cosh(ax) sin(bx))
1
n²+1
8
and (ii) Y = Σ
n=1
(-1)n+1
n² + 1
(d) Find the corresponding Fourier coefficients in the Fourier series for y(x), which is periodic and
satisfies the differential equation
d²y
dx² - y = f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0388bcf-4f8c-4d4a-b19c-3c3492446ed7%2F3a4c7af5-7bf7-4185-ab55-726503b9509f%2Fdjwuons_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let the function f be defined by
for - < x < π and satisfy
f(x+2) = f(x).
Recall that cosh x = (e* + e*)/2 and in the following you are given the indefinite integral
So
1
a² + b²
for constants a and b.
cosh(ax) cos(bx)dx=
f(x) = cosh x
∞
(i) x = Σ
X
n=1
(c) By evaluating the Fourier series for appropriate values of x, find the following sums:
(a sinh(ax) cos(bx) + b cosh(ax) sin(bx))
1
n²+1
8
and (ii) Y = Σ
n=1
(-1)n+1
n² + 1
(d) Find the corresponding Fourier coefficients in the Fourier series for y(x), which is periodic and
satisfies the differential equation
d²y
dx² - y = f(x).
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