By using partial fraction and 2nd shift theorem, show that, 3 3 L-1, ls(s² + 4) -H(t – 4) –H(t – 4)cos(2(t – 4))

Q: F(s) = .L{cos 2t H(t-) + (912+2t-1) H(t– 2)}.

A: We will find out the required value.

Q: Consider the first order ODE y' = √y² – 9. Use the fundamental existence-uniqueness theorem (on page…

A: The given first order ODE is .The aim check whether the ODE has a unique solution or not at the…

Q: Let r(t) = (sin(t), cos(t), 6 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane…

A: Given vector…

Q: h(t) = / e -3(t-T) cos(27)dr. This is the convolution of two functions f(t) and Consider g(t). That…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find f(x) = f a-1x1 0 the Fourier a-1x1, Hence prove transform Ixl <a , Ixla that 1 (sin t t 0 2 of…

A: Given f(x)=a-x,x&lt;a i.e., -a&lt;x&lt;a                   =0,         x&gt;a i.e., x&gt;a, x&lt;-a…

Q: f(t) = 8 + 6t+2t², for- n<t<π, Show Transcribed Text and extend to a 2π periodic function.

A: The given function is ft=8+6t+2t2  for -π&lt;t≤π. To extend the function to a 2π periodic function.…

Q: Find y2(x) given y₁ (x), the W(y₁ (x), y2(x)), and y2(0). (a) ут(1) 1, vv \y 1, 2) 11 y210) (b)…

A: b) Given that y1x=3x-1, Wy1, y2=-3x2+2x-3 and y20=1. We have to find y2x using the Abel's theorem.

Q: 25. Find the harmonic conjugate of u = In|z| and corresponding analytic function f (z) = u + iv.

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Q: v=e2r-y cos (y– 2x) Obtain the value of of the relation дхду A 8e2r-y sin (y– 2x) B - 6e2 -y cos(y–…

A: Option (C) is the correct.To solve this question first we take the partial derivative with respect…

Q: Th nction f(2) = (2z3 + 8z) (z – 2i)(z + 5i)2 has a pole at z = -5i. :Select one True False

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Q: Verify that u(x, y) = x² − 6x²y²+y¹ is harmonic everywhere and determine its harmonic conjugate.

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Q: If v(1, y) is a harmonic conjugate of a harmonic function u(1,y) is also a harmonic function. show…

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

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Q: The function f (x) = 10 + 2 cos(14x) + cos(11x) + 2 sin(7x) − cos(4x) + 5 cos(3x) is called The…

A: Solution: To find the length ∣∣f(x)∣∣ of the Fairy Godmother curve…

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: Let u(x, y) = x² - y² and v(x, y) = x³ - 3xy². Show that u and v are harmor functions but that their…

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

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Q: Classify the zeroes (according to order) and isolated singularities of (2² - 1)e¹/² cos (TZ) (z + 2)…

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Q: (4) Let f₂ = df/az and ƒz = df/az. Recall ƒ = u + iv, the notation f is used for the complex…

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Q: (c) L-¹ 2s 14 { (8+3)(8 + + +28+5) 4e-3s -1 s² (s+4)) (d) L-¹ {

A: As per the policy of bartleby the provisions is to solve only one question at a time  but here  I am…

Q: 15. (a) (i) Find the Z-transforms of cos and 'n(n+1) no A (ii) Using convolution theorem, evaluation…

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Q: Determine the integral f(z) dz around the clockwisely oriented triangle with the vertices ₁ = -1, 22…

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Q: : Find Fourie trans form? alt)= 5 rect(134) @ F[214-2) +²0+] e @ F[x(++) cos(3+)] Sext] © F[z(t)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: You deposit $2000 in an account with an annual interest rate of r (in decimal form) compounded…

A: Please refer to the solution in next step.