The Fourier series of a function f(x) defined on -7, 7] is given by 1 4+ cos z + 4. 1 cos 2x + 42 1 cos.3z + 1 cos 4r +.... 44 13 | ((=)* dz = The value of the Integral 193 1) 12 481T 2) 30 385 3) 24 496 4) 30

Q: Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

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Q: 2. Given f(x) = sin 2x, 0<x<n find a) Fourier sine series (set up and integrate) b) Fourier cosine…

A: We use the formula for solve this

Q: (1 -5<t<0 is The Fourier Series expansion of f(t) =11+t 0<t<5 (-1)" nnt nnt sin 22- f(t) [[(– 1)" –…

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Q: ded as a Fourier se of x, then

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Q: (3Vr + 2e) dx.

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Q: Derive formula (2) on page 601. cosucos v 5lcos (u – v) + cos (u + v)]

A: Given equation is cosucosv=12cosu-v+cosu+v. cosu-v=cosucosv+sinusinvcosu+v=cosucosv-sinusinv

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: Suppose that the Fourier series expansion for function { 2 cos x, if - Ħ< x < 0 f (x) = if 0 < x < T…

A: Given fx=2cosxif -π&lt;x&lt;0sinxif  0&lt;x&lt;π

Q: Q4] Find the Fourier series for the following periodic function defined as t² -t² f(t) = { 0 < t < π…

A: We have to find the fourier series of the function

Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

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Q: (b) Prove that the Fourier series for f(x) is: 1 f(x) = ²0 (si -20 (sinx + sin3x +sin5x + ...) TU

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Q: The best approximation of f (x) = cos(3 + x) by a %3D Fourier polynomial of degree 1 is 1) F(x) =…

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Q: If F is an odd function, and has a period of 2n such that, F(3)-π- x within ]0 , π[ i) Develop F in…

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Q: (2) Prove that TT/2 S tane Z coś 0 (1 + tano) ² 11 #la

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Q: Let f(x) = 1- x on 0, T|. The Fourier cosine series of f on 0, T is a) None of these (-1)" cos (! b)…

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Q: Compute 2π *cos (+5€40) do. COS 0

A: Given integral: ∫02πcosπ3+5eiθ dθ Solve the given integral. Concept used: Trigonometric sum formula:…

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: Fourier series f(x)= x sinx 2 xe (7)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: |1] What is the value of the period (T) for Fourier Series of the function f(x) = { -x - 2<x<8…

A: We find period (T) of given function

Q: 3: You are given that the Fourier series expansion of f(x) = x2, x € (-7, 7) with period 27 is +4…

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Q: Show that the Fourier series of frx)= x² in El, 1] is x2 (-19^ 4 CosnTx, and hence show that n2 n=}…

A: Given function is fx=x2 in -1,1. We have to show that the Fourier series of fx=x2 in -1,1 is…

Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

Q: What is the complex Fourier series of the function f(t) = cos t? Hint: if you're confident, you can…

A: We find the complex Fourier series of the function f(t)=cos(t).

Q: The complex Fourier series of a function f(x) is given by 1+in einz. Then | (2)e* dz = %3D 1+ in4…

A: The complex Fourier series of a function fx is given by  fx=∑n=-∞∞1+in1+in4einx…

Q: Find the Fourier series of period 2n for the function scos x – sin x, -n<x< 0 lcosx + sin x, f(x) =…

A: Sketch the graph of given function.

Q: * ;The answer is What is the value of (an) for Fourier Series of the function f (x) = {: 0<xS n a) 1…

A: Given: fx=0,   -π≤x≤0 1,   0&lt;x≤π

Q: The area of the region inside r= 2 + sin and outside r= 2-2 cos 0 is given by

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Q: 00 f(x) =a0+ an cos n=1 is called 2 laplce transform aO Besseal polynomial ,O .b fourier series.cO…

A: The Fourier series of the function f(x) is given by. f(x)=a02+∞∑n=1{ancosnx+bnsinnx}, where the…

Q: 4) Let be the periodic functionf (t) = t +1 (0 <t < 2), with period T = 2 a) Draw the graph of f(t).…

A: The main objective is to find complex form of Fourier series of f(t).

Q: 13) Expand fit) in Fourier series in the interve) (-2, 2) when fit) = -zst <o

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Q: 7 b) Prove the identity 2 cosxt sinco (1 + COS X) =1

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Q: 9- a) b) C) e) The Fourier series of the function f(x) + 2 8 0 -4 = 8, -4, -π<x<0 0<x<T at the point…

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Q: The complex Fourier series representation of a periodic function of period 27 is given by 00 Fs(t) =…

A: Here c0 is not defined. Using the given information cn=an+bn |cn|=√(a2n+b2n) Phase=arctan(bn/an)

Q: expanded as odulus of x, the 1-e

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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 Fourier series [o, 2w] an <x<π fcx) = TくXく 2w

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Q: Q4) Considering fanction of fla)=x, & -ncacrR a) Is this function odd or even b)epand fantion sine…

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