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obtain the Fourier series expansion f(z)=1/z about the point z=1
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- Suppose that f(t) is periodic with period -T, 7) and has the following real Fourier coefficients: a2 = 3, аз — 3, b2 = -3, b3 = 0, ao 4, a1 = 1, b, = 2, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coefficients for the following functions: (i) The derivative f'(t) ao = , a1 = -1 , az = -6 , az = -9 b, = 2 , b2 = -6 bz = (ii) The function f(t) – 2 ao = , a1 = , az = 3 , аз — 3 b1 = 2 , b2 = -3 bz = (iii) The antiderivative of (f(t) 2) (with C 0) ao = , a1 , a2 = 3/2 , аз 1 b1 =-2 b2 = 3/2 b3 = (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) ao = 2 , a1 = 1 , a2 = 6 , аз — 3 b, = 2 b2 = -3 b3 = 3 (iv) The function f(2t) an =2 , a1 , a2 3 , a3 3 b, = 2 , b2 = -3 b3 = 0Let f(e) = { , 1 ISI< 2n Find the Fourier series of f (x) over the interval [0,27]Find the trigonometric Fourier series for the square 2n-periodic wave defined on the interval [-11,1]: f(x) = {0, if-SX<0 f(x) = {1, if 0Recommended textbooks for youAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill EducationAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education