Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)). Explain why (V x F). ds = 0.

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Q: [3 0 -9 -25 -33 We want to determine if the columns of A span R². Let A = To check this we add times…

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A: The exercise follows using multiplicative property of Legendre symbols

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Q: Problem #11: Consider the following differential equation, 5xy" +(2+x) y + y = 0. = Note that xo - 0…

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Q: 7. Show that if n is odd, then p(4n) - 2 q(n). =

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Find the eigenvalues of A, given that A = and its eigenvectors are The eigenvalues are 0 -1 -1 0 -2…

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Q: Solve the system of differential equations x₁' = 6x₁ + 0x2 – 2x3 x2= 1x₁ + 1x2 + 2x3 x3 = 1x₁ + 0x₂…

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Q: 2) Use the quadratic formula to find the exact solution to the given equation. (Enter your answers…

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Q: Let Q(x) = 143x² – 34x2 – 34x² – 36x1x2 – 36x1x3 — 72x2x3. Find a unit vector x in R3 whose first…

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Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4 x² defined on (x₁, x2) = R². The function f (x1, x₂) is…

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Q: S 4. Find the Taylor series of cos x and show that it converges to cos x for xER. 5. Repeat the Q4…

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Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4 x² defined on (x1, x2 ) = R². The Hessian matrix of f…

A: The objective of the question is to find the Hessian matrix of the function f(x1, x2) = 5x1^2 +…