The Fourier series representation, FS(t), of a function f(t), where f(t + 10) = f(t) is given by FS(t) = a = 1.25 an= a 2 + an cos b₁ = In this particular case the Fourier series coeffcients are given by ant 2(-1)" TUR + b₂ sin nat 5 4(1-2(-1)") 72²7² Compute the Fourier series coefficients for n = 1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS,(2.5) correct to 3 decimal places. Enter the values in the boxes below. Enter a correct to 4 decimal places: Enter a correct to 4 decimal places: Enter a correct to 4 decimal places: Enter b, correct to 4 decimal places: Enter b₂ correct to 4 decimal places: Enter by correct to 4 decimal places: Enter FS (2.5) correct to 3 decimal places:

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Q: Answer f(x) = 1-2e-3iz, x € [-67,67] p = 67, C₂ = 0 if n 0,-18 co = 1 c-18 = -2.

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A: FSt=a02+∑n=1∞ancosnπt4+bnsinnπt4a0=1.5an=4-1nnπbn=51-2-1nn2π2

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