(12) The coefficients (a, ) of the Fourier series of the function f(x)= x;-7

Q: using fourier series fur the function 2X Conclade that S(2n=1)-= so b) T 6. C) T? 8.

A: Your expression of series is typing mistake, it should be 1/(2n-1)².

Q: 0,-T <x<0 tsen x, 0sx < T 9. f(x) =

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Q: Consider the function f(x) = = −1, X, 1, −2 < x < −1, −1 ≤ x < 1, 1 ≤ x < 2. (a) Sketch the graph of…

A: Graph of the function and it's series

Q: Find the coefficient of x° in the power series of this function f(x) = (1–2x)2

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Q: f (x) AN X

A: The given problem is to find the Fourier series expansion from the given graph of the following…

Q: 5. Determine the half range Fourier cosine series for -{- f(x)= 7-X

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Q: Consider the folowing +9, 1S O, + 2) - a) (a) Skench the graph of the given function for three…

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Q: The question is to find a power series for the function centered at c f(x) = 5/(5-x) , c = -3

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Q: x) = cos in the interval of (-T, 7) %3D

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Q: Q5): Determine the Fourier series of the function f(x) = 1 - x² in the interval [-1, 1].

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Q: 3/ Determine the Fourier series of the function shown. y=2 2- 2 -27 2т х 0 27

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Q: Obtain the Fourier series of the following function (-x-3 -1 S(x) =x -35x5-2 -25xS-1 Isrs2 -x+3…

A: Given the function  fx=-x-3-3≤x≤-2-1-2≤x≤-1x-1≤x≤111≤x≤2-x+32≤x≤3

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Q: +00 (-1)"(3n + 4) 23n+3(n + 1) Differentiate the function f (x) = x ln(1 + x) to determine the sum…

A: The product rule of the differentiation is as follows: ddxu(x).v(x)=du(x)dx.v(x)+dv(x)dx.u(x)

Q: O Let f (x) be a function which is represented by the power series f(x) =E(-1)"-1)". n3 What is the…

A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

Q: Q (4)- Find Fourier series for the function: - 2 <t <0 2 f(t) = (4 for for 0 <t< 2

A: Given that, f(t)=-2-2&lt;t&lt;040&lt;t&lt;2 The aim is to find the fourier series. The formula for…

Q: Find the real form of the Fourier series for the function f(x) =- \x| in (-1, 1) and then obtain…

A: Fourier series of a function f(x) in the interval -L≤x≤L is defined as  f(x)=A0+∑n=1∞An cosnπxL+Bn…

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: - 1< x < 0 0 < x < 1' (e* 3. Find the Fourier series of f(x) = {". f(x) = f(x + 2).

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Q: Find a power series for the function f (x) = x2/(1 + x3)

A: We have to find the power series for the function f (x) = x²/(1 + x³)

Q: Find the Fourier series of the function f(x) f(x)=x+|x|        (-π<x<π) i- Tell the function…

A: Given: The given function f(x)=x+x ,(-π&lt;x&lt;π)

Q: 22/Find the Fourier series for the following function? (SM) r)=x for

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Q: Using complex form, find the Fourier series of the function f(x)=signx={−1,−π≤x≤01,0&lt;x≤π.

A: Fourier theorem states that any function can be decomposed in terms of trigonometric functions like…

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: f(x) equals      {0, -5 <x<0}                         {3, 0<x<5}   Write the fourier series…

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Q: Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between…

A: Maclaurin polynomial of degree 4 is P4x=f0+f'0x+f''02!x2+f'''03!x3+f404!x4.

Q: 1. Fl the fourier series representing, f(x)=x, 0<x< 2 and sketch its graph from x =-4 to x=4n.

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Q: 0, -T < x < 0 f(x) : X, 0 < x < T Obtain the Fourier series representing the given function and…

A: Given :-  The given Fourier series : fx = 0           ,    -π&lt;x&lt;0x           ,       0…

Q: 25- A) Use series to express the function f(x) = coshx.

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Q: Q2. Find the Fourier series for the function f(x) = ›>-6 for for 0<x<π π < x < 2π

A: Sol