Question

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)

Answer #1

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

Find the Fourier Sine integral representation for the
function
f(x) = x, 0<x<a (and zero otherwise)

1. Find the Fourier cosine series for f(x) = x on the interval 0
≤ x ≤ π in terms of cos(kx). Hint: Use the even extension.
2. Find the Fourier sine series for f(x) = x on the interval 0 ≤
x ≤ 1 in terms of sin(kπx). Hint: Use the odd extension.

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.

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

Find the:
(a) Fourier cosine series
(b) Fourier sine series
for the following shape using half range expressions
f(x)=x^(2), 0 less than or equal to x less than or equal to
1

Consider the first full period of the sine function:
sin(x), 0 < x < 2π.
(1) Plot the original function and your
four-term approximation using a computer for the range −2π < x
< 0. Comment.
(2) Expand sin(x), 0 < x < 2π, in a
Fourier sine series.

Find the Fourier Transform of the following, Show all
steps:
1- f(x)=e^(-6x^2)
2- f(x) is 0 for all x except 0≤x≤2 where f(x)=4

Find the Fourier series of f(x) as given over one period.
1.
f(x) =(0 if −2 < x < 0 and
2 if 0 < x < 2 )

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