Use Lagrange multipliers to find three positive numbers whose sum is 51 and the sum of whose squares is as small as possible. (Enter your answers as a comma-separated list.)

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Q: For the differential equation (x2-4)y" + (x- 2)y' +2y = 0, a regular singular point is:

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Q: the summation of the two power seriesE=12nc,x"-1 + By writing E=16c,x"+1 = 0, we obtain: in%3D1 2c,…

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Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x? + z?.

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Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

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Q: Solve the following system of differential equations. dw = -w + 52z dt dx 2x dt dy = 2w – 4y + 2z dt…

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Q: х — у 3. f(x, у, 2) %3D y? + z? а. f(3, —1, 2) b. с. d. f(2, 2, 100)

A: Solution

Q: (d) Ralston's method.

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Q: fined the genral solution 8) (D + D,)'u = 0 %3D

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A: Here [B] is inverse of [A] which means [A] is inverse of [B].  Also we know that, for any square…

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: diff. eqs. =2 y" – 2x y + 2 y =x³sinx

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Q: 3 4

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Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

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Q: For the differential equation (x – 4)y" + (x– 2)y' + 2y = 0, the singular points are: O None of them…

A: Here we use the basic definitions of singular point

Q: O (Ax^2 + Bx + C)e^(2x) O (Ax^3 + Bx^2 + Cx)e^(x) O None of them O (Ax^3 + Bx^2 + Cx)e^(2x)

A: Particular solution

Q: Let n be a positive integer and f(n) = -53n109 n51 + 53. %3D Then f (n) is

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Q: 25.2 Solve the following problem over the interval from x 0 to 1 using a step size of 0.25 where…

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Q: Symbols Write the equation of the tangent line to the graph of y = (6x2 - 6x + 3)(1 + 2x) at x = 1.…

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