Question

A function is defined over (0,2) by f(x) = { 1/2x 0 < x and x <= 1, 0 1 < x and x < 2 We then extend it to an odd periodic function of period 4 and its graph is displayed below. The function may be approximated by the Fourier series f(x) = a_0 + sum_{n=1}^{infinity} ( a_n cos(npix/L) + b_n sin(npix/L) ), where L is the half-period of the function. Use the fact that f(x) and f(x) cos(npix/L) are odd functions, enter the value of a_n in the box below. a_n = , for n = 0,1,2,... Hence the Fourier series made up entirely of sines. Calculate the following coefficients of the Fourier series and enter them below in Maple syntax. b_1 = b_2 = b_3 = b_4 =

          A function is defined over (0,2) by
f(x) = { 1/2x 0 < x and x <= 1, 0 1 < x and x < 2
We then extend it to an odd periodic function of period 4
and its graph is displayed below.
The function may be approximated by the Fourier series
f(x) = a_0 + sum_{n=1}^{infinity} ( a_n cos(n*pi*x/L) + b_n sin(n*pi*x/L) ),
where L is the half-period of the function.
Use the fact that f(x) and f(x) cos(n*pi*x/L) are odd functions, enter the value of a_n in the box below.
a_n = , for n = 0,1,2,...
Hence the Fourier series made up entirely of sines.
Calculate the following coefficients of the Fourier series and enter them below in Maple syntax.
b_1 =
b_2 =
b_3 =
b_4 =

A function is defined over (0,2) by
f(x) = 1/2x 0 < x and x <= 1, 0 1 < x and x < 2
We then extend it to an odd periodic function of period 4
and its graph is displayed below.
The function may be approximated by the Fourier series
f(x) = a0 + sumn=1^infinity ( an cos(n*pi*x/L) + bn sin(n*pi*x/L) ),
where L is the half-period of the function.
Use the fact that f(x) and f(x) cos(n*pi*x/L) are odd functions, enter the value of an in the box below.
an = , for n = 0,1,2,...
Hence the Fourier series made up entirely of sines.
Calculate the following coefficients of the Fourier series and enter them below in Maple syntax.
b1 =
b2 =
b3 =
b4 =

Added by Daniela A.

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