Assume that u and u are continuously differentiable functions. Using Green's theorem, prove that Uz JE v|dA = fudv, Uy D where D is some domain enclosed by a simple closed curve C with positive orientation.

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Q: 3. Solve the Differential Equation: (x² + y² + 3)dx - 2xydy = 0

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Q: 6. if x C y. (a) (b) Let R = {a: a is a cut}.Let x, y, E R. We say that a <y if and only Prove that…

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Q: (EAF) → (~G →H) FA G :. E → H

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Q: 2 + 53 - 12 9us - 12 - UII ugg + y UII UTI - - - UTTII = 0. uxy6uyy = xsiny. Buyy xy. 2ury = cos 2.…

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Q: One of the following is an allowable change of parameters t = Þ(0) = 8³ +0 This answer t = Þ(0) = 0²…

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Q: 26. The quartics c²y² = x(x - a)³ with a held fixed.

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Q: The graph shows a region of feasible solutions. Use this region to find maximum and minimum values…

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Q: 3. A triangle has vertices at A = (2,-1,-4), B = (0,5,-2), and C= (0, -3,0). Find the measure, in…

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Q: Verify that the given functions y1(t)=t, y2(t)=t?^t are solutions to the homogeneous equation…

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Q: - the D.E.: xdy + (2y – x³y² sin(x))dx = 0

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Q: Problem 3 Let = N and A = P(N). Let P: A → [0,1] be a function with the property that for all A,BEA…

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Q: 1 -[-3 3] 5 f A = of B. and AB = | -3-1 1 17 determine the first and second co

A: AB=-3-11117 B=1-3-35 We have to find A

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Q: For function f(x) = x² ln x, let x。 = 1, x₁ = 2, and x₂ = 3. Use divided difference al-gorithm to…

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Q: 2}

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Q: [2] True or False? If false, find an example to justify. If true, quote a THM to justify. (a) For…

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Q: x'- 2x/t=21², x(-2) = 4. 2te²x = 3t¹ + e², x(1) = 1, using the substitution v= e²r.

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Q: 3. Suppose that P is invertible and that A = PBP-¹. Solve for B in terms of A and P.

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Q: 1. Use deductive reasoning to show that the following procedure produces a number that is three…

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Q: 4. Solve the D.E.: dy dx 1+x³ -3x²ydx 1+x³

A: Given differential equationdy-dx1+x3=-3x2y dx1+x3