Find the sum of 1+++t using Fourier series expansion if f(x) a when [0,T] and 2 T-x when [ T, 2 T].

Q: Show that the Fourier series of the function g(x) = |r| on the interval |-7, 7| is s(-) -- 1 cos…

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Q: 3) Find Fourier series expansion of he funchion f(x) - T/2 Śn 2o %3D cos n

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Q: find the fourier series of f(x) = x^2  in the interval [0,2pi]

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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: Find the Fourier Series expansion of (-) - 3 < x <0 f(x) = %3D 0<x < 3 And f(x) = f(x+6).

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Q: Obtain the Fourier series in [-m, n] for the function : x, if -n<x<0, f(x)= 2x, if 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: Find the Fourier series expansion for: x2 f(x) = x + ,-n <x < n 4

A: Let us consider the function f(x) on the interval [-L,L] is obtained as…

Q: f(x) = e"

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Q: A. Find the Fourier Series af x)= -x- = X+Y 0 4x<

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Q: 0, f (x) : -T < x < 0 sin x, 0 < x < T

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Q: Expand f(x) =eax in a fourier series in 0<x<2π

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Q: Expand in a Fourier series f (x) = a², 1 < x < 1 then find 2' n4

A: Given that fx=x2 and find Fourier series in -12&lt;x&lt;12. The Fourier series is…

Q: Assume that there is a Fourier series converging to the function f defined by х, —2 <х < 0, f(x) =…

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Q: Expand the function f(x) = x² - 2x + 1 in the interval [ -1, 1] using Fourier series formula.

A: The Fourier series expansion of the function f(x),defined over the interval [-L,L] is given by…

Q: The Fourier series for the funetion f(x)= 5x* -x+2, -T<x<T contains

A: f(x)=5x^2-x+2 is a even function

Q: · Find the Fourier series of, - 2< x< -1 f(x) = -1<x <1 (1 1< x< 2

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Q: find theral form or fourier Series for f(x) = x+\xl in (- T, JJ) and then abtain Complex form?

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Q: Find the Fourier Series of : F(x) = nx for -n/2 sxS n/2 for 1/2 Sx s 3n/2

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Q: Determine the Fourier cosine series expansion of f (x) = sin(r2) – cos(Tx) on the interval [-1,0]

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Q: Find the Fourier series of the piecewise smooth function (-x, -2 < x < 0 f(x) = 1 %3D 0<x < 2 2' on…

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Q: find the fourier series of f(x)=[pi-x/2]^2, <-x<-2pi   hence deduce that…

A: Given that f(x)=π-x22,0≤x≤2π. To fourier series of any function is given by,…

Q: solve for the Fourier series f(x)=x^2 in (-1,1)

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Q: Find the Fourier sine series expansion of the funct f(x) = x² + 5, 0 <x < n.

A: Fourier Sine Series: The Fourier sine series of a function fx in 0≤x≤l is given by fx=∑n=1∞bnsinnπxl…

Q: Find the fourier series expansion in the f(x)=2x+1_range of the [-1,1

A: Given a function fx=2x+1 with range of -1, 1.

Q: Calculate the Fourier series for the function f(r) = 6(r –- 1) – 6(r+ 1) when -2 <aS2 and is…

A: The function is odd so there will be no constant and cosine terms.  The Fourier series will be:

Q: Find fe(), the Fourier series expansion of * € [-L, 0), * € [0, L], where k and L are positive…

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Q: Determine the a, of nth partial sum of the Fourier Series of the periodic function f(x) = -9x + 6,…

A: Formula of a0 for the fourier series is given bya0=1π∫-ππf(x)dx for the interval [-π,π]

Q: 0, Expand f(x) = -A<x<0 in a Fourier series. * -x, 0 S r<a

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Q: (2, if -2x <0 f (x)=- x, if 0<x<2 %3D

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Q: : Obtain the Fourier series for the function: (4x+1 if – n <x< 0, f (x) = |1–5x if 0<x<r.

A: We will find out the required value.

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

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Q: expand f(X)=eax in a Fourier series in 0<X<2pie

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Q: Find the Fourier series representation of sin 2x, -n <x < -1/2 -1/2 < x < 0 sin 2x, 0 < x <n. f(x) =…

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Q: Find the Fourier series expansion for f(x) = x+-nsxSn

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Q: Expand f(x) = x,0 < x < 2n in a Fourier series if (a) the period is 27, (b) the period is not…

A: We have to expand fx=x2, 0&lt;x&lt;2π in Fourier series if: a the period is 2π:

Q: Express f(x) = cos wx, - <x<n, as a Fourier series. Hence prove that 2w 2w coton = 2w + 12)(a)²-22)…

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Q: Find the Fourier series expansion of the function f(x)=x2 knowing that…

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Q: Find the coefficient of sin nx in the Fourier series expansion of f (x) = x² (0 <x < 2n)

A: We find the coefficient of sin(nx) in the Fourier series expansion of f(x)=x2(0&lt;x&lt;2π).

Q: 8, Find Fourier series of the function in the Fig. • -2 (XS-1 -1<Xく 1くxく2 fo) -1 T=4 ー3 ー2 子 -2 スナ

A: Fourier series formula for any function: f(x)=ao+∑n=1∞(ancosnπxL+bnsinnπxL)

Q: : Develop f (x) in the Fourier series, if defined as: (i): f (x)= 6xsin 5x, – n < x < n.

A: We will find out the required Fourier series.

Q: Expand the function f(x) = 2e-2x in a complex Fourier series over the interval-n<x< Do thi %3D…

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Q: 4. Expend the given function in the Fourier series in the given interval [5x-1, -A <xs0 f(x)=.…

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Q: (3-2х, - nSx<0, f(x)= - |0,

A: The given problem is to find the Fourier series of given periodic function and also to sketch the…

Q: Find the Fourier series of f(x) = x − x2 on [−1, 1].

A: The Fourier series of the function f(x) is,f(x)=a02+∑n=1∞ancosnx+bnsinnxwhere, a0=1π∫-11f(x)…

Q: Find the Fourier series of f(x) = V1- cos x in the interval (0, 2n). Hence, 1 1 deduce that Σ -- 2…

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Q: Obtain the Fourier series expansion for the function of period 2π as follows f(t)=2-t/π,   -π<x<π.

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Q: Find the sum of 1+1/1^2 +1/3^2 +1/5^2 +⋯, using Fourier series expansion if f(x) = a when [0,π] and…

A: Given:- The sum 1+112+132+152+............ if f(x)= a when 0,π and 2π-x when π,2π

Q: Determine the bn of nth partial sum of the Fourier Series of the periodic function f(x) = -9x + 6,…

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