The function f is defined by -1 if – T< x < 0, f(x) 1 if 0 < x < T, and f has period 27. (d) Calculate the Fourier coefficient, b,. (e) Write the Fourier series of the function f.
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- If f is the Fourier series of g(x) = = f(x) = 32(-1)"+1 n²-² [16-r², What does f(-4) equal? f(-4) What does f(-2) equal? f(-2)= What does f(0) equal? f(0) n² What does f(1) equal? f(1) What does f(4) equal? ƒ(4) FIT 4 -4< <0 0A periodic function f(x) is defined by f(x) = x² + 3 for –2Solve for Fourier coefficient, Ssin x 02x27 f(x)= 0 T >x 22n cosx sec x + cosx csc csc² x csc? x secx cos? x cos x cos x § f(x)dx _ ? If f(x)* , then 1For fourier series of periodic function how is the first picture = 2nd picture? able to provide the derivationf(x) = {x, 0<x<pi} {2x-x, pi<x<2x}Determine the fourier series for the function defined1 Find Fourier cosine transform of f(x) =< -1 0Question 4 Let f be a function that has derivatives of all orders on the interval (3, 5). Use the values in the table below and the formula for Taylor polynomials to give the 4" degree Taylor polynomial for f centered at x = = 4: f(4) f'(4) f"(4) f"(4) f(4)(4) -4 10 8 -5 a) O-4 + 6 (x – 4) + 10(x – 4)² + 8(x – 4)³ – 5(x – 4)* b) O-5x4 + 8x³ + 10x² + 6x – 4 c) O-4 + 6 (x + 4) + 10(x + 4)² + 8(x + 4)' – 5(x + 4)* d) O-4 + 6 (x – 4) + 5(x – 4)° +x – 4° –- – 4) 5 (x- 4)* 24 4 e) O-4 + 6 (x + 4) + 5(x + 4)² + 5 x +4)° – x+4* 24 5 f) O- 24 4 + '+ 5x? + 6x – 4 3The Fourier coefficient a, in the Fourier cosine series of f(x)%3D2X, 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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