3) Find Fourier series of the following functions: a) f(x) = x², -1
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![3) Find Fourier series of the following functions:
a) f(x) = x², -1< x <1 and f (x + 2) = f(x)
b) f(x) = |x|, - n< x < n and f (x + 2n) = f (x)
%3|
- 2 < x < 0
c) f(x) =
and f(x + 4) = f(x)
1,
0 < x < 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9aaebd5c-1654-4eda-8ff2-248691f00fc6%2Fe2f9f34a-ce0f-4348-852c-6f162106cf77%2Fa9wu2o_processed.jpeg&w=3840&q=75)
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- The Fourier series of a function f (x) defined on [-1, n] is given by 1 9 + cos x + 1 -cos 2x + 92 1 -cos 3x + 1 -cos 4x + ... 93 The value of the integral (f(x))² dx5. Find the Fourier Coefficients for the following functions on the given intervals: (a) f(x) = x³ (b) f(x) = x³ [-n, 7] [-1, 1) 0 -27Graph and find the Fourier coefficients of the following functions f (x): - T/2 < x < Tn/2 1/2 < x < 3n/2 1 a) f(x) = { -1 b) f(x) = { "** -πA periodic function f(x) is defined by f(x) = x² + 3 for –2d) Write the corresponding Fourier series of f (x). A periodic function of f (x) is given by [0, f(x)={-x-7, f(x+27). - T < x < 0, 0(b) Using the answer to Part (a) and without using Theorem 2.2.4, find the real Fourier series of the function f(x) = -2x 2r-8 if 0 < x < 2 if 2 < x < 4 and f(x+4)=f(x).If f is the Fourier series of g(x)= √3, [16-², -4 < x < 0 then 0≤ < 4 f(2)=¯ + 2 [(0) cos (1 x) + ( ) sin (7-²)] 2 What does f(-4) equal? f(-4) What does f(-2) equal? f(-2) = What does f(0) equal? What does f(1) equal? What does f(4) equal? (0) f(1) = ƒ(4) = *1. Express f(x) by the Fourier series where f(x)= {, 2, -7f(x) and g(x) is periodic and has a Fourier Series representation: f(x) = cos(6*pi*x) g(x)=sin(6*pi*x) z(x) = f(x)*g(x) Find a0, a1, a2, a3 for z(x). Simplify as much as possible!Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,