(i) At x = 1, the Fourier Series of f(x) = converges to: (A) 0 (B) 1 (2-2x, -1

Q: b. Find The Fourier series for the function defined by -n <x <0 0sx<π SA + x f(x) = {".

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Q: b)If (x) = f(x+2n), find the Fourier series expansion of (0, -n SxS0 x, 0 SxSn f(x) = %3D

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Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: Q2: Find the Fourier series corresponding to the function -k -n<x<0 S(x)3D k 0<x<T

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Q: If f(x) = |sinx| in (-1,1) is expressed as Fourier series, then the coefficient of sin5x is 5 ?لكر…

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Q: Q1: Expand in a sine-Fourier series: f(x)=x,0 < x < 1.

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Q: Q4: Consider the function L(a) as an even function and expand it using an appropriate Fourier…

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Q: Let f(x) = 1- x, -3 ≤ x ≤ 3, f(x + 6) = f f(x). (a) Find the real-valued Fourier series of f.

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Q: 3. Expand the function f(x)=x (4-x²) in the interval -2 ≤x≤2 and period f(x+4)= f(x) to the Fouriér…

A: Solution :-

Q: Q2. Find the Fourier series for the function f(x) = |x-x² for −1 < x < x<π]

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Q: Find the Fourier series of the 2-periodic extension of the function defined on (-1,1) by f(x) = x…

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Q: B/ Find the Fourier series of the function f (X) = x +n within the range -n < x < n

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Q: Q2: Find the Fourier series expansion of the function f(x) = xsinx for < x < 2n.

A: Given fx=xsinx We know fx=a02+∑n=1∞ancosnx+bnsinnx

Q: (b) At x = 0, the Fourier series of x - 2, -1 <x S 10, converges to: (A) -2 (B) –1 (C () The colut.

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Q: Q2: Expand f(x) in a sine-cosine Fourier series TT 20, f(x) = { -<x< '4' π ¹4, 1<x<T. 4

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Q: (a) Calculate and write the expansion Fourier series of the corresponding functions: 0 <x <T f(x) =…

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Q: ƒ (x) = X (1+6x)²

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Q: f(x) = n² – x² 0<xくT

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Q: a) Find the Fourier series of function, f(x) given below: 0₂ for -≤x≤0 x²; for 0≤x≤ which is assumed…

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Q: 5. (a)Find the Fourier sine series for f(x) = x³ – n²x on the interval [-7, T]. (b) By plugging in a…

A: For (a), We need to find the Fourier sine series for the function, f(x) = x3 - π2x on the interval…

Q: Find fourier series of f(x) =|xl, -2<x <2

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Q: f(x) = sin (2x)| -T≤x≤0 0<x<*

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Q: use fourier series to solve

A: We can solve this using formula of Fourier series

Q: (8) (a) Compute the Fourier sine series for the function f such that f(x) = x² on the interval [0,…

A: Fourier series is the expansion of a periodic function as the sum of linear combinations of sine and…

Q: a Let W ER a + b+ c = 0 Prove that W is a subspace of R Find a basis for W and state the dimension…

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Q: Calculate the Fourier series of the function f(x) = x on the interval [−2,2].

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Q: Find the Fourier series of the function if -4 <x< 0 f(x) S(x + 8) = f(x) %3D if 0 <x< 4

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Q: Find the Fourier series to represent f(x) = x/2 (0 < x <2pi.)

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Q: Expand f(x) = -X X if -π < x < 0, if 0 < x < π, in a Fourier series.

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