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- 5. Convert the function f(x)=eux and f(x+2) = f(x) defined in the interval (-π < x < π) to the complex Fouriér Series.Graph 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) = { "** -πProve that f(x)={-3x if -pi<x<0, 3x if 0<x<pi is an even function using fourier series expansion.Suppose a function f(x) = x between 0 and 1, and f(x) = 0 elsewhere. Solve for the fourier transform g(k) of the original function f(x).5) If f(x)= x?; f (x +4)=f (x) b. The coefficient n in this Fourier series is : 2 (-1)". (na) (-1)** . (na) (-1)- cos d) 2 a) b) 0 c)A 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).Find the Fourier series of the function f(x), of period {-π,π], defined by: f(x)=1 if x≥0; f(x)=0 if x<0 graph the solution1. Express f(x) by the Fourier series where f(x)= {, 2, -72 Denote the Fourier series of f(z) = { -x, 0Recommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning