3. Let f : R R be a periodic function with period 2a. Define F(x) = f(t)dt. (a)Is F(x) always a periodic function? Under what condition is F(x) periodic? (b)Assume that f has Fourier expansion ao +E1(an cos()+b, sin(")). What is the Fourier coefficient for F(x) (assuming it is periodic)?

Q: 16. (a) Obtain the Fourier series for the 27-periodic odd function f (x): x (T – x) on [0, T]. %3D…

A: please see  the next step for solution

Q: 21 Date... w******** Q. Find the Fourier Series od (x) = X -즐 <x<플

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A: Note: Since you have posted multiple questions, according to the policy we are only allowed to solve…

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Q: 4. Find the Fourier series for the Function f (x) = |x| ,When -nsXS T.

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A: a)The given function is, f(x)=x+1,-2&lt;x&lt;01,0&lt;x&lt;2And the period is 2-(-2)=4

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A: fx = x3,period : 2π,Interval : -π, π

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A: Sol:- Fourier series of function fx on interval -L≤ x≤ L is defined as: x=A0+∑n=1∞ An·cosnπxL+∑n=1∞…

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A: There is no correct option of first six option, if there is another option then ok.

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Q: H.W: Find Fourier series expansion of the periodic function -7<x<0 -k f(x) = { k Period=2n 0<x<A

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A: Half range cosine series expansion

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Q: 5. Find the term representing the third har- monic for the periodic function of period 27 given by:…

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A: the fourier series expansion is as follow

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Q: [2] Find the Fourier series of the function f(x) = sin(4x) {ain(kx) -T≤ x < -π/2 -π/2<x< π/2 π/2 ≤ x…

A: Solution