Question

Find the Fourier Sine integral representation for the function

f(x) = x, 0<x<a (and zero otherwise)

Answer #1

Find the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

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

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 coefficients A(ω) and B(ω) in the Fourier integral of
the function f(x) = e^ −3x if x > 0 and f(x) = 0 if x < 0
.
Full working please no short cuts, I want to see the full
integration by parts.

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.

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

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

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

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

Fourier Series
Expand each function into its cosine series and sine series for
the given period
P=2
f(x) = x, 0<=x<5
f(x) = 1, 5<=x<10

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