8. Which of the following are orthonormal s 1 A = {U₁ = (₂0₁2), U₂=(2,0, B = { U₁ = (2,0, ₂2), U₂ = (2,0, c = { ₁ = (₁ 3₁3), U₂ = (0), 3' D = (U₁ = (0₁) ₂ = (0, c) C, d) D. a) A, b) B,

Q: A) L{t//4} : (5/4)! a+5 B) L{u-2(t)} C) L{e"u(t)} 8- 5 3! D) L{t*e"} = E) e{icm (;)} 5Cos s(s – 2)…

A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

Q: a) Which of the following systems of ODES is autonomous and dynamical? where ty₁ = e-sin(₂), y₂ = ₁…

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Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the…

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Q: L[u(t – 3) (1²4' – 9 4')] = 81e-4s 2 (s-ln 3)3 8 (s-ln 3)2 64e-3s 2 (s-In 4)3 6. (s-In 4)2 81e-4s 2…

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Q: Let h(u) = (u +3) (u - 4) Determine the most general antiderivative of h. (u +3)(u — 4)du = -

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Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

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Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x.…

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Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

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Q: 12.) Let h: IR³ -> IR5 and g: IR² -> IR³ be IR² -> IR³ be given by hcxy. 2) - (xyz, ex* x sin(y),…

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Q: P(E2) = P(E3) =s, P(E4) = P(E5) =/20, P(Es) = '/10, P(E7) = '/5: A В E1 o E 2 o E4 E5 o E3 o E7 O E6

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Q: Q4. (a) Give A = 2xy â, +3â, +z'yâ,, calculate v.AdV as shown in Figure Q4(a). A, (0, 1, 1) (0,0, 1)…

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Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

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Q: Let (w, x, y, z) = wxy + x² tan z and a = (1, -2,3,4). Then w(a): .₂(a) = -6 -2 8 60 -8 1-1 2 , (a)…

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Q: 19. A particle moves in the plane from (-2,5) to the y-axis in such away that Ay = 3*Ax . Find its…

A: Given data is : A particle moves in the plane from -2,5 to the y-axis  ∆y=3×∆x Let point on the…

Q: 1. R= {(1, 1), (2, 2), (3, 4), (5,9)} C ZX Z 2. R= {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m)…

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Q: (kx 3. -){(kx-ky +kz).

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Q: O a. 1-1/e O b.0 O c. 1+1/e O d. Divergent O e. 1

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Q: Let f(x, y, z) = x³y5 + z4 and x = (a) Calculate the primary derivatives of, of of дх' ду'dz' (Use…

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Q: QUESTION 22 Not yet answered Man Calculate the value of (1+2i)2 and then use this value to find the…

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Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: Let Ci and co be arbitrany canstants. Geneial solutian to the hamogencus dfferenti al oquation 1692…

A: Given differential is Cauchy Euler's differential equation

Q: := rye" find z²y}e" (ry +1) O None of these Option 3 rye"" (ry + 2) ry²e# (xy + 2) Option 2 Option 1

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Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: W.Find A' for the given cholce of U. 1A (3,6, 9) U (x/0<x$ 10 A 2. A = (1, 2, 3) U = (0, 1, 2, 3, 4,…

A: From the given information we find the A compliment .

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: , Which of the following processes is stationary? A) An MA(1) process with 0 = -1.6 B) Y, = 58.46 +…

A: The stationary process is

Q: Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for…

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Q: (A) Given that n(A')=20, n(B')=40, n(A'∪B')=50, n(∪)=80, find A ∩B (B)  Given that n(A')=70,…

A: A)n(A')=20n(B')=40n(A'B')=50n(U)=80

Q: What are the roots of the characteristic equation of the following system? da dy 3x +2y-z dt dz 2x +…

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Q: Prove that: 1st equation = 2nd equation Equation 1 Sn = a + (a+d) + (a+2d) +...+ [a+(n-1)d]…

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