2) Find the (complex) Fourier transform of 1-2, if r| S1, F(z) 0. if |피> 1, I COS I- Sin z and hence evaluate

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: -* is -. р Show that the finite sine transform of 1 . TC

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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: I hope the solution is understandable and not abbreviated

A: Given: fx=xe-x, x>0 We have to find the Fourier Sine Integral presentation of the given function.

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: 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: -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: 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: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: Find the Residues of given points 1 at z = nt sin z

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Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: 37nx Find C2{sin (*} (Finite Cosine transform) O A. 6L O B. 4L - 5TT OC. 2L - 5T O D. O E. None

A: Find C2sin3πxL

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0

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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: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

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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: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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

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Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: x+yi dz (az + b)" if a = 4, b = 6, c = 10502, n = 3, x = 1, and y = 6. Then, find the imaginary…

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Q: Evaluate the integral s sin³ (3x) cos³ (3x) dx . Osin¹ (3x) sin (3x) + C 12 18 -

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Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: The function (f) with a period of 2π is defined by: f(x) = cosh (x - 2π)  if x∈[π ; 3π] a)…

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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: a5 8 Suppose you are given the following Fourier coefficients for a function on the interval [−π,…

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Q: 5.6.3. Let f(x) 16 interpolation points. Then, plot f(x) along with the resulting (real)…

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Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: Qi Write the order and degree of the given. ODE'S.check either these equations aye nón-linear. Also…

A: Consider the given function. y''+x2y-2y'=sinx As the maximum order of the derivative is 2.  So, the…

Q: 3) Let f(x) =) () Find the fourier Senies of fx nd skatch the the sum function on [-37,37). +++*…

A: we know Fourier series f(x)= 90+∑ n=1∞ancosnx+bnsin nx…