Find the 2 * 1 vector such as (x1, x2)′ that minimizes w = x′ Ax − 10. What is the value of w at the minimum? [Hint: recall that a condition for minimization is that the derivative is equal to zero].

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A: We know that ∆y=f(x+∆x)-f(x). So,             ∆y=f(x+∆x)-f(x)      =f(5+0.4)-f(5)      =5·…

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A: Linear approximation

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

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Q: Consider the Freudenstein and Roth test function f(x)= f;(x)² + f2(x)², xER?, where fi(x) =-13+x1…

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Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

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A: Note:-    as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find the orthogonal trajectories of Vy = cx = CX

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Q: 3. Find an admissible extremal for the problem of minimizing J[a] {Gi² + xi + x + à} dt with x(0) 1…

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Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4x + 5y = k (2) 4х — 5у 3Dk…

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Q: Find the linear approximation to f(x, y) f(6.11, 4.17) f(6.11, 4.17) = 5, xy at the point (6, 4,…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: By utilizing Gradient Descent where initial x1=x2=Dx3%3D0, What is the approximated min. point of…

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Q: What is the linear approximation for any generic linear function y=mx+b?

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Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

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Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

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Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: For functions f(x,y,z) = 5xyz and g(x,y,z) = x2 + 3y? + 4z2 – 7. write the Lagrange multiplier…

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Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

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