Find the two coupled Euler-Lagrange equations giving the stationary path of the functional S[y₁,92] = [ da [y² + 2y² + (2y1 + 32)²].

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Q: Problem 4 Let Let F == [cos z cos y, 1 - sin z sin y] and C is given by r(t) = [cost, 2 sint], 0≤t≤.…

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Q: Question 2: Find a general solution to the following differential equation in the form of a power…

A: Find a general solution to the following differential equation in the form of a power series.

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Q: Let an be recursively defined by ao = 2, an+1 = Show that an converges, and find its limit. 3an 5an…

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Q: log(2+x)-x2 sin x 1+x²n Check the continuity of the function f(x) = lim- 11-0 (A) Conitinuous at x=1…

A: Given functionCase-1When f(x)=log(2+x); |x|<1Case-2Whenf(x)=Case-3Case-4when x=-1

Q: 2- Find the inverse of the following matrix using Gauss elimination method 3 A=[-²2 5 -2 -3 B 1 -1…

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Q: Use the simplex method to solve the following simplex problems. a) Maximise 6x1 + 9x2 + 6x3 subject

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Q: 2. (a) Trace the curve y²=(x-2) (x - 5)².

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Minimize Z = y +y² + y² Subject to constraints: y₁ + y2 +y3 ≥ 15 and y₁, y2, V3 ≥ 0

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Q: Does the set of all functions that vanish at x = 0 and x = L form a vector space? If it does,…

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Q: Determine the approximate slope of the tangent to the curve f(x) = 2x-1 x+2 at x = -1, to 1 decimal…

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Q: . Define a linear transformation T: R² → R² by ere G = 3)₁0<0< cos (0) -sin(0) cos(0) cos(0) T(x) =…

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Q: Q2: In the two-tank mixing process shown in Fig.(2), x varies from 0 lb salt/ft³ to 1 lb salt/ft²…

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Q: X f(x) 0,0 1,0 0,5 1,0 15 20 2,119 2,910 3945 3,945 5,72 2,5 8,695

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Q: According to the Rational Zero Theorem, list all possible rational roots of P(x) = 8x² − 3x² + 4x −…

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Q: (3). Define a linear transformation T: R2 R2 by →> where G = ( 3) ₁ 0 <0 < cos (0) - sin(0) cos(0)…

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Q: Calculate the following integral: 27 de a+bcose where a> b>0

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Q: 02: Find a solution of: a² + 2y²-y-2B=0 a²-8y² + 10ß = 0 a² 7γβ Using Newton Raphson. When the…

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Q: Given the following table: X f(x) 0,0 1,0 0,5 2,119 1,0 2,910 1,5 3,945 2,0 5,72 2,5 8,695

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Q: - 2 (410gx = log √ 2² ) + log ³√/x² Write as a single logarithm.

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Q: Sales of Orange computer have grown steadily during the past 5 years: Year Sales 1 450…

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Q: When creating a left-endpoint Riemann sum on the interval [90.6, 391.4] using 40 rectangles, the 7th…

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Q: Let u4 be a linear combination of {u₁, U2, u3}. Select the best statement. ● A. {U₁, U2, U3, U4} is…

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Q: 13/ Find dy/dx, if x =2 sin (1+34), y=2+² when t = = =

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Q: Suppose fn(x) = nx(1-x)" for x = [0, 1]. Show that (fn) converges pointwise but not uniformly to the…

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Q: Expand the function f(x) = x sinx, as a Fourier series in the interval - < x < π.

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