Question

- Calculate the Fourier series expansion of the function:

*f(x)*
*=**1/**2(**π-x)* *,* when *0
<* *x* *≤* *π *and

*f(x) = -*
*1/**2(**π+x)**,* when -*π*
*≤* *x* *< 0*

Answer #1

Compute the complex Fourier series of the function f(x)= 0 if −
π < x < 0, 1 if 0 ≤ x < π
on the interval [−π, π]. To what value does the complex Fourier
series converge at x = 0?

Find the Fourier series of the function f(x) = |x|, −π/2 < x
< π/2 , with period π.

find the Fourier series to represent the function
f(x)=x-x^2 where x{-π,π}

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

Find the half-range cosine Fourier series expansion of the
function f(x) = x + 3;
0 < x < 1.

Consider f(x)=sinx, 0 ≤x≤π
a) Express double expansion of f(x) with a formula.
b) Find expansion to Fourier series of f(x).

Write the Fourier cosine series for f(x) on the interval 0 ≤ x ≤
π. Parameter c is a constant. f(x) = x + e −x + c
(b) Determine the value of c such that a0 in the Fourier cosine
series is equal to zero.

Find the half range cosine Fourier series expansion of the
function f(x) = x + 3, 0 < x < 1
Need full work shown (formulas/ every step)

Expand the function f(x) = x^2 in a Fourier sine series on the
interval 0 ≤ x ≤ 1.

fourier expansion, piecewise function.
f(x){ pi , -1<x<0
-pi , 0<x<1

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