Question

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.

Answer #1

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

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

Find the derivative of the function.
(a) f(x) = e^(3x)
(b) f(x) = e^(x) + x^(2)
(c) f(x) = x^(3) e^(x)
(d) f(x) = 4e^(3x + 2)
(e) f(x) = 5x^(4)e^(7x+4)
(f) f(x) = (3e^(2x))^1/4

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)

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

a. Let f be an odd function. Find the Fourier series of f on
[-1, 1]
b. Let f be an even function. Find the Fourier series of f on
[-1, 1].
c. At what condition for f would make the series converge to f
at x=0 and x=1?

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

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

find the following for the function f(x)=3x^2+4x-4
a. f(0) b. f(3) c. f(-3) d. f(-x) e. -f(x) f. f(x+2) g. f(4x) h.
f(x+h)

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

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