Q1) Find Fourier transform for the following functions: a) x(t) = 3 + (sin2wt)² b) y(t) = 5. (e-6t). 8(t – 8) + 6u(t + 8) %3D

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

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Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

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: The function re* sin(8x) is annihilated by the operator

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Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

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Q: 9x dx VI-9x -/1-9x2 +C -1 arcsin 3x + C + C 3(x3 – 3x)

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Q: Find two fourier expansions for the function h(r) = sin(r). In one expansion, all the sine terms…

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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: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: S sec² (7t) tan² (7t) √1 – tan² (7t) dt

A: Given integral:- ∫sec27ttan27t1-tan27tdt

Q: Calculate Sin(5x)=-√(2)/2

A:

Q: The value of (-1+√3 i)^(1/3) is О 2 exp((2TU/7)^i ) 2 exp((2/3)^i) 2 exp((2T/9)^i) 2 exp((2T/5)^i)…

A: We need to choose correct option. As per Bartleby's guidelines we can solve only one question from…

Q: Q5: Find the complex form of Fourier expansion of the following function: f(1) =e' -1</<+1

A: Sol:- Complex Form of Fourier series of function fx on interval -L≤ x≤ L is defined as:fx=A0+∑n=1∞…

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

A:

Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: 2. Perform the indicated operations: (2D2 - 3D+5) (xcox x- 3) a. b. (D3+2D- 4) (e*sin x + e2x)

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Q: Find the Fourier coefficients of the function f(x) = sin(10x) cos(x).

A: Given function is Noted that for a function for which fourier series exists, it is of the following…

Q: Q4) Find the Fourier coefficients corresponding for the below function, then answer the following…

A: To find the Fourier coefficients corresponding to the function below, f(x)=x2, 0&lt;x&lt;2π Is this…

Q: a) Find the Fourier Transform of f(x) = = √2πx³ex, 0<x< 6

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q4) Find the Fourier coefficients corresponding for the below function, then answer the following…

A: The Fourier series of a function f(x) with a period 2c is given by f(x)=a0+∑n=1∞ an cosnπxl+∑n=1∞ bn…

Q: 1. g(t) 3D 4x(t)e/2n4(0) + Зу(t) 2. g(t) = 2y(t) 3. д(t) %3D х(t —2)у(4t) 4. g(t) = 8(t) * y(t) dt

A: Fourier transformation is given by: x(t)=X(f)y(t)=Y(f) 1.)   g(t)=4x(t) ei2π4t+3y(t) Apply Fourier…

Q: JO the MacLaurin polynomial of degree 7 for F(x).

A: Given,          F(x)=∫0xsin6t2dt.