The Fourier transform of the function f(x)=1 ; |x|<2, is 2 sin 2p (c) F(p)=. 2 sin 2p (a) F(p) = sin 2p (b) F(p) = P 1 (d) F(p) = sin 2p (f) Non of these

Q: If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is…

A: Introduction: The Fourier Transform may be used to deal with preliminary boundary cost problems at…

Q: Q4) Find Fourier transform of the functions: 1)f(x)= nxl, x π 3)f(x)=xe-x1, x ER 2)f(x) = 4)f(x) =…

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Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

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Q: Evaluate f{ [sec (x) + csc (x)] + sin ()} dx : (2)]? + sin (팔프)}dz O a. tan (x) In |csc (2æ) + cot…

A: To solve the following integral

Q: Consider the function f(x) = x + 2 sin(x) for - <x<. Find (f-1)'c0). (5-1)'(M) = help (numbers)

A: Note that for x=0, f(x)=0 Then we will find f'(0)

Q: 1 (-0 + 7) - 1 Sketch a graph of the function f(0) = -3 sin(-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: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

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 coefficients of the periodic function f(x)=x-2x², (-<x<n); f(x+2) = f(x)

A: We have to solve by Fourier series.

Q: -3 if 0 6 The Fourier sine transform of f(x) is sin 3w a) 6 2 (sin 6w b) -3 1-cos 6w с) —3 -cos 3w…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Let f(x)=2x-3,g(x)-5x, and h(x)=x2 what is the sinpliest fornm of h(x)*g(f(x))

A: Explanation of the solution is given below...

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: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: Let 7'(t) = (3+ 4t, cos(t), 6e*) and F(0) = (7, 2, 5). Determine 7(t). †(t) = (, , )

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Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: 4) dependent Show that the following set of functions is Linearly independent or linearly f₂(x) = 3,…

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Q: State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms…

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Q: If f(Z) = cos (3z2) then the simplify form of f(2) is: A) f(z) = i log(3z² + iv9z+ – 1 B) f(Z) = -i…

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Q: BIJ Compute the derivative f'cts for 5./ fcto= log (x

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A: Give function is fx2+sinx=x we differentiate it, f'x2+sinx2x+cosx=1⇒f'x2+sinx=12x+cosx f'x2+sinx…

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A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: What is the range of f(x)-¹ = cos¯¹(0)₂ A C D [-] 2 2 [0, π] [-1,1] (-∞, ∞0)

A: Given query is to find the range of the function.

Q: times the Fourier transform of f(x) provided that the first (n – 1) derivatives of f(x) vanish as…

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