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Q: 4. Every normed space is a pre-Hilbert space.

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A: Given the differential equation is                        on      and

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A: The given initial value problem,.We have to find the solution to the IVP.

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Q: Problem 5. Evaluate a²2² ds, where S is the part of the cone 2² = x² + y² that lies between the…

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Q: The maximum value of f(x, y) subject to the constraint g(x, y) = 210 is 6200. The method of Lagrange…

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Q: g(x)= ind 211 g ()

A: We are givenFormula

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Q: Find Euler's equation for the following functional b G[x(t)] = [(x¹². 1= 22x²+x²)dt; x(a) = a, x(b)…

A: The Euler Lagrane equation  of the functional is  .

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Q: e2-s 2-¹ (6-3)) - O [(-1/3) +e^(3(t-1))/3] e^2 U(t-1) O [(-1/3)+e^(4(t-1))/3] e^2 U(t-1) O None of…

A: As per the guidelines I am answering only one question at a time.Formulawhere

Q: A = 2 -1 -2 3 -1 1 1 -2 0

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Q: (a) What does the Gibbs free energy represent in terms of work? (b) Give two examples of…

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Q: P-1.37 Consider a nonsingular matrix A. Given any matrix E, show that there exists a such that the…

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Q: Let f = C(R/Z; C), and for n= 0,1,2,... define 2/₁₁ (2) cos(2x)da; by = 2(a) sin(2xnx)da. 0,1] Show…

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Q: Consider the sequence facx) = 1²x (1-x) for x E FR Ⓒ Evaluate S fn God dac Evaluate lim ( facoes doe…

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Q: True of False. Explain. Let α ∈ C be algebraic over Q of degree n. If f (α) = 0 for nonzero f (x) ∈…

A: be algebraic over of degree . for nonzero .

Q: 1. Use Newtons method to solve the following system of non-linear equations. Show three iterations…

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Q: Use the Gauss-Jordan reduction to solve the following linear system: X2 + 4x3 = -2 5x2 + x1 4x1 -3x1…

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Q: . Evaluate dS, where S is the paraboloid y = 9-x² - 2² together with its cap when y = 0. (7/6)…

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 0 0 S S -2 -√√4-x²…

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Q: Example Determine the unit tangent vector for r(t) = (t,t³,t5) at the point P = (1,2,3).

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Q: the output y are related by Consider a system L{f(t)} = y(t), for t≥ 0, where the input f and y"(t)…

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Q: 3. Luke and Leia are participating in a space race. Let F(t) be the position of Luke and Leia at…

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Q: X x= X = -2.7 x x².7 2 X = ? find X

A: We are givenRemember :

Q: x² - y² Define f(0,0) in a way that extends f(x,y) = xy- x² + y² to be continuous at the origin.

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 0 1 ILIR 1+…

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Q: Consider the ring Z/nZ, where n is a natural number. The elements of the ring are the residues of…

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Q: Consider the curve r(t) = (t²- 4t, -3t + 1, −2t² + 5t+4). This is called a planar curve, which means…

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