0, The Fourier series of the function f(z) = is given by %3D 5x, 57 10 5. cos 5z +...]+[sin z – 2 1 1 1 [cos z + 1 sin 2x +sin 3x +...]. 3 cos 3x + 4 32 52 The minimum error between f and the Fourier polynomials (trigonometric polynomials) of degree 1 equals 573 1) 25( 24 573 2) 24 3) 25( 3 8. 4) 3. 8. 5x3 5) 5( 51

Q: Find the fourier expansion for the function whose definition - - <x <- 2 x, - 2 (x) 0, <x< 2 2

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Q: 5 sin [ -5TT X<ST %3D otherwise

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Q: Find sec42x -dx tan 2x A --—-—-cot²2x-—-—-cot³21+ C 16 cot82x) (4sec22x-1) B -(cort2x) 4 12 11 1 C)…

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Q: the Fourier series of the al ternating using Function Fins D. -T《メ《。 get the sinn result of the…

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Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a

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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: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x&gt;1

Q: "(등 -2) + ain (품 + 22) The simplified form of cos 22x) + sin O V3 cos 22x + sin 22x O v2 cos 22x + 2…

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Q: 2) Find the Fourier transforms of: a) b) f(x) = cos(ax), where a > 0. f(x) = x² cos(ax) + x sin(ax),…

A: Since the given problem has multiple sub parts, as per our company guidelines we will solve only the…

Q: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

Q: T (b) fo 6 sin 20 cos² 20 ӨР

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Q: Q6) Find the Fourier transform of the following signals and draw the amplitude spectrum for each a)…

A: Given that,

Q: To show that rπ/2 sin" x cos" x dx: (m - 1) (m- 3) ... × (n – 1) (n - 3)... (m + n) (m + n - 2) (m +…

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Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

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Q: If Z-1/v2+i/v2 then the value of conjugate of Z^5=?* O cos(3n/4) O 2sin(5n/4) O 2cos(5n/4) cos(5n/4)

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Q: for 0sxs 10 for r> 10 sin(x) for 0srs2x for x> 2x

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Q: The output voltage of a generator is given by v- 168 cos 2rft - Express the voltage as the sum of a…

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Suppose a 3rd order constant coefficient ODE has a characteristic equation that had 3 distinct…

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Q: Problem 2. For the function defined by if -22x20 0<x<2 52 - 2 f(x) = 2x+2 sketch the 4- Period…

A: As per the question we are given a piecewise defined function f(x)  with period 4 and we have to…

Q: A periodic function is defined as: F(t) = {"_2 - nst< 01 0st<nS a) Sketch the graph of the function…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: sin2xdx 1) S7 o sin+x+cos4x

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Q: Consider the period 4 function -2 <x < 0 0 <x < 2 f(r+4) otherwise. f(r) · 2 - x (a) Sketch three…

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Q: Consider solving x²V1-x² dx using trigonometric substitution. Which of the following is true? a. 2…

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Q: The complex exponential Fourier coefficients for the periodic function x(t)=t, 0<t<2 is:

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Q: Prove that Fourier cosine transform of f(x) = cos(x), 0<x<3 is: 1/27 (³ sin 3(p-1), sin 3(p+1) p-1 +…

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes features relying on…

Q: Evaluate L{e (sin3t + cos 5t)}. 3. s+5 A. +. (s+5)+9(s+ 5)+25 3. s-5 В. (s-5)-9 (s-5) +25 s+5 C.…

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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: Integrate 0 1 S √1 1-4x2 dx using a trigonometric substitution. sin-¹ (2x)√1-42²+ C 0 1 -sin-¹ (2x)…

A: The given integral is sqrt(1-4x2).

Q: Use the triangle to express 8 as a function of y. 10 08 = sin() 0 8 = sin n-¹(10) 0 0 = cos 1¹ (1)…

A: We can find the correct option in the below steps.