Question

fourier expansion, piecewise function.

f(x){ pi , -1<x<0

-pi , 0<x<1

Answer #1

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

Find a Fourier Series expansion for the function f(x)= xcos(3x)
on the domain from x = [-pi,pi]

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

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

Expand the Fourier Series.
f(x) = 1- x, -pi < x < pi

Find the Fourier sine expansion of
f(x) = x for 0 < x < 1
2- x for 1 < x <2 (at least the first 4 nonzero term)

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)

Consider the piecewise defined function
f(x) = xa− xb if 0<x<1. and
f(x) = lnxc if x≥1.
where a, b, c are positive numbers chosen in such a way that
f(x) is differentiable for all 0<x<∞. What can be said about
a, b, and c?

Find the Fourier Series of the function: f(x)=0, -5<x<0,
f(x)=3, 0<x<5 with a period=10.
Write briefly about how such a series expansion could be used?
For example, in digital to analog conversion?

Find the real Fourier series of the piece-wise defined
function
f(x) = Pi+x -2<=x<2

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