Handwritten fast Please.. 2) Use Cauchy Residue Theorem to calculate the inverse transforms a) F(s)= 1/s b) F(s)= a/(s^2 + a^2) c) F(s)= 1/((s+a)(s+b))

Q: (a) For n20 write out the first four terms of the sequence a(n) =(-3)" and then use the definition…

A: Given that, xn=-3n

Q: 5. Residue theorem Use the residue theorem to compute (a) ro∞ t2+1 dt.

A: Given integral is∫0∞t2+1t4+1dtThe integral is computed using Residue theorem as shown below.

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

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Q: press the improper rational transform: 3 4 X(z) = 1+ + + 1 3 ms of a polynomial and a proper…

A:

Q: +(n) = 3 (²³-9x² +33m - 18 enfor 1) Ⓒincreasing in (-0,0) (Ⓒineressing M- L decreasing in (2,8) in…

A: The function is given by:-Since, the natural log is present in the function.Domain of the function…

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: L[2t2 + 5 – 3 cos nt), t > 0

A: We use the Linearity property and table of Laplace transform to find the answer of the given…

Q: 0. Reciprocal Substitution (x´ - x')"3

A:

Q: Etample T4 Find the inverse finite cosine transform f (x) if (2nn cos 3 where 0<x < 4. F(n) = (2n +…

A: Inverse finite cosine transform

Q: 2. (a) For n 2 0 write out the fint four terms of the sequence z(n) 3(-3)" and then use the…

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Q: Find the inverse Z transform of X(Z) = z^(-2) + 2z^(-3) + 5z^(-4)

A: Formula: The inverse z-transform of the function X(z)=z-m is δn-m. Given: X(z)=z-2+2z-3+5z-4 To…

Q: Expand f(z) =1/z2 in power of z+1

A: The given problem is related with Taylor series expansion of a function. Given that,…

Q: ii) using the Fourier Transforms, Calculate dx. Jo (4x*)(9+x*)'

A:

Q: Find Fourier transform of the n-th derivative f(n) of a smooth function f with fast decay at…

A: We know that the Fourier Transform of a function f(x) is possible when the integral ∫-∞∞f(x) e-iωxdx…

Q: 2s – 7 - F(s) = %3D (s – 4)(s + 6)

A:

Q: Calculate the Taylor polynomials T2 and T3 centered at x = a for the function f(x) = In(x + 1), a =…

A: Given function is  fx=lnx+1. To calculate Taylor polynomials T2 and T3 centered at x=a, we write…

Q: dR/dt = a * R / (b + R) - c * R dS/dt = d - c * S (a,b,c,d are all constants) what is the…

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Q: do the inverse laplace transforms of the rational function F(s)=(s-2)/s(s^2 -4s+8)

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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: Transform of f(x) = (1-) in Find the finite Fouirer Cosine (0, 7)

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Q: chain rule to differentiate the following 1 y = sec 4 sec* (√x + 3)

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Q: 12. Let f(a) be a function with f(1) = 2, f'(1) = 6, f"(1) = -12. Which of the following is the…

A: according to bartleby guide line we do only first part of multiple 12)  given  f(1)=2  , f'(1)=6,…

Q: Let. a 3 = (-) = -(1) - P = ( ) 5 and a) Find Fourier Coefficient of b with respect to a . b) Find…

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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: Fis) = 1ls +28 %3D H4)=L*[F(s]? (s+2) (s+5)

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Q: Solve the Inverse Laplace Transform 6 1 F(s) = ((25 + 3)² + = -) 0 ² e 5s 3

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Q: Orthogonalize {1, t, t²} in P₂ (R) with 1 (f, 9) = ["ª, f(x)g(x) dx. -1 Then normalize each one so…

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