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

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Q: ded as a Fourier se of x, then

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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: H.w. Fourier series for Ex1 fex) = ーnくxくo アーメ 0くxくn

A: Since the solution is lengthy we solve only the first problem.  If you want the solution to the…

Q: 9₁¹ = = Σ m=3,5,7.... (2) sin() a 2 ( 2² h ²2 (1-m²)) 2ma² 2 4maa 0 =√√√(4) (3 + a ħ² (sin (3x) +…

A: Consider the provided expression, φ11=∑m=3,5,7...2αasinmπ2π2h22ma21-m2φm0 In the given expanded form…

Q: 2. Height travel by the rocket in first 6 seconds is given by s = (5 103) || In (T00-4) dt- 180…

A: I am attaching image so that you understand each and every step.

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: 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: Sine a IF fox)= cesx Find Fourier series のくズくズ

A: Fourier series is significant in mathematics, specially in the signaling process. Every periodic…

Q: Find the Fourier sine series for f(x) = on 2)=7 On - -L≤ x ≤L.

A: f(x) = x on –L ≤ x ≤ LFind the Fourier sine series for f(x).

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: Fourier Series of 2 – on the interval [-7, 7] 8(–1)" cos() cos( 2 + Σ 3+ 72 -2n=1 (-1)" cos (nz) n2…

A: In the given question we have to choose the correct options from the given options. In the 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: 5. Expand the following function in Fourier series where f(x)=x+r and show that 1 =1-- + 3 1 1 + 1 5…

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Q: 9. If a, =1.57, a, -(-1) -11. b, --)" f(t) and period f(t) =f(t+4) up to n=2 is then the Fourier…

A: Fourier series of the function

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

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Q: The Fourier series for a periodical sawtooth wave is O O −sin (wt) + sin(2wt) — ½ sin(3wt) + sin…

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Q: how 300/sin(120+Θ) become 300/cos(30+Θ)?

A: Topic:- trigonometry

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: Q2) Answer the Following: 1- Find the Fourier series for the following function f(x) = { 2, -HAX<H…

A: Note: I am solving question 1)

Q: 4.w. Fourier series For Exイ fcx). ースくくくo アーメ 0くxくn

A: As u asked for multiple question only first question is answered, for remaining question please…

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

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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: f(t) = < ² F(E + 2") if 0<t < n for all t has the complex Fourier series (-1)"(in²n² + 2nn – 21) +…

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

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Q: Find Fourier sertes [o, 2] an 2) fex) f Cx) = Sin X ニ

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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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