1. Prove that (a) ▼ × (▼ƒ) = 0 for any C² function ƒ : U → R;

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Q: Consider the initial value problem given below. dx dt = 3+tsin (tx), x(0) = 0 Use the improved…

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Q: INSTRUCTIONS Analyze the response of the system using MATLAB 2x"+x'-x=27cos (2t) +6sin(t); x(0)=-1,…

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Q: 2. Determine whether x4 +x³+x² +2 and x³ +1 are congruent mod (x² + 2) in Z3[x].

A: 2)  Let  and  in      We  have  to check that whether…

Q: Exercise: Let u = [3, −2, 1], v = [1, 1, 1] and w = [2, -2,0]. The area of the parallelogram formed…

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Q: Problem 3. Let u be a smooth solution of Lu aªÏ µij V = |Vu|²+ Au². Show that Lv ≥ 0 in № if λ is…

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Q: 0881 144 (1)| +| (2) |log3 2 (1) = (2)

A: Properties are used.

Q: Given the three basic functions: /(x) = sin x f(x) = log x f(x) = 2^x Determine how and which of the…

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Q: (a) S = {(a,b): (b) S = {(a,b): a € Z+, b € Z+, and a b} a € Zt, b € Zt, and 3|(a + b)

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Q: Solve Cauchi problem x²y" - 4xy' + 4y = 0. y(1) = 0, y'(1) = 1

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Q: Letf : R² → R be defined by f((x, y)) = 8x + 5y + 1. Isf a linear transformation? a. f((x₁, y₁) +…

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Q: From the options below, select those sets which are functions from {1,2,3} to {7,8}. {(2,7), (1,8)}…

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Q: Let G be a graph. Prove that G is Eulerian if and only if G has an orientation D where D is an…

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Q: Find the flux of the vector field F = xi + e6xj + zk through the surface S given by that portion of…

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Q: 4. Let X be a metric space. Show that if every continuous function f : X → Ris bounded, then X is…

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Q: ~M³(N-O) 1. 2. NOP 3.0~p /M prove using the rules of implication

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Q: a. The dimension of the subspace His b. Is {14x² + 12x + 11, 9x² + 8x +7,- (22x² + 20x +17)} a basis…

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Q: Linear algebra: please solve q18 correctly and handwritten. Theoram is also attached

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Q: 14. It is desired to find particular solutions of the differential equations given below. 1. y"+y' =…

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Q: ~M³(N-O) 1. 2. NOP 3. 0~p ✓ Conclusion /M premises prove using the rules of implication

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Q: Problem 4.4a. Produce a BVP for the Laplace equation, describing the equilibrium heat distribution…

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Q: Find the maximum value of f(x1, x2, x3) = 6x₁ + 7x₂ + 2x3 subject to the following constraints. S x₁…

A: subjected to constrain

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Q: Consider the multiplicative group Z4547. a) How many primitive elements does this group have? b)…

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Q: for a fixed n>1 Show that all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

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Q: 5 d²q dt² + 10 dq + 1 q = 25 sint dt 0.1

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