the function defined in the interval by and extended periodically has period and is illustrated below. find the classical fourier series in the form use pi for . give the general form the coefficients .

Respuesta :

The corresponding, co-efficient is  f(x) ≈ A°/2 + ∈∞ [AK Cos ( kπx) + Bk sin (Kπ) x ] .

What is co-efficient ?

An element's number of atoms is indicated in part of the chemical formulae of the reactants and products. A little whole number called a coefficient can be seen in front of a formula in a balanced chemical equation.

What is interval?

The range within which the true value is most likely to fall is known as a confidence interval. These numbers are derived from data that was utilized in the statistical study.

P(x)= ∫ 0 xe (-1,0)

        ∫x xe (0,1/2)

        ∫0, xe (1/2, 1)

A₀= 1/2x ∫ f(x) dx = 1/ 2(1) ∫ f(x) dx = 1/2 ∫ xdx = 1/2 ∫x/l

A₀= 1/4 [1/4] = 1/16

Ax= 1/6 ∫ f(x) cos [nπx/l] dx -1/1 ∫f(x) d cos [kπx/1] dx

Ax = 1∫ k. cos (Kπx) dx

Ak= (x sinπx/ kπ . kπ) - 1/2 - 1/kπ ∫sin kπxdx

Ak = (1/2 sin kπ/2 - 1/kπ) +  1/ (kπ)² (cosπx)²

Ak = 1/ 2kπ sin kπ/2 +1/ (kπ)² ( cos kπ/ 2-1)

corresponding forier series is

f(x) ≈ A°/2 + ∈∞ [AK Cos ( kπx) + Bk sin (Kπ) x ]

Therefore, the corresponding, co-efficient is  f(x) ≈ A°/2 + ∈∞ [AK Cos ( kπx) + Bk sin (Kπ) x ] .

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