Solve the following optimal control problem with the given boundary conditions: 1/f ² w ² min_ J = = 2 s.t ₁(t) = x₂(t), u² (t) dt x₁ (0) = 0

Q: Find the goveming equation and associated boundary conditions by minimizing the functional, I.…

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Q: Suppose you want to find the minimum of f(x) = x² - 2x + 7 as a function of using gradient descent.…

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Q: Calculate all of the critical points of the function: f(x, y) = x² xy + 2y? %3| is a relative…

A: f(x,y)  = x^2-xy+2y^2 f'(x)= 2x-y f'(y)= 4y-x for critical points : f'(x)=0 then 2x-y=0  f'(y)=0…

Q: 2. Find the particular solution if dx dt 4 x² - 9 a) x(0) = -1, b) x(3) = 3, c) x(0) = 3. d) x(0) =…

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Q: dy Show that the given function y = −t cost — t is a solution of the IVP t = y + dt t² sint…

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A: In this problem, we are dealing with a mortality function that determines the mortality rate for…

Q: Find the gradients and hessians of the following multivariate functions. Justify your answers. (a)…

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Q: 9 R? (x + R)² dt2 dx x(0) = 0 , %3D de (0)

A: Given: d2xdt2=-gR2x+R2, x(0)=0 , dxdt(0)=v0

Q: solve by optimal control: 3. 1 [²(ux − u² − x²) dt - subject to x' = x+u, x(1) = 2. max

A: Given,The integral maxSubject to .Aim: To solve the integral by optimal control.The Euler Lagrange's…

Q: 9. Verify that p(t) = te/50 satisfies the condition p(t) dt = 1

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Q: Let the demand and supply be dP (a, ß, y, 8 > 0) Qa = a – BP –Y Assuming that the market is cleared…

A: Please consider the handwritten solution.

Q: 8.xy² If u = and error in x, y, z be 0.001, compute the maximum absolute and relative z³ error, when…

A: Given equation be u=8xy2z3 error in x, y, z be 0.001 Now ∂u∂x=8y2z3, ∂u∂y=16xyz3, ∂u∂z=-24xy2z4  and…

Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: 2) a) Find the general antiderivative of the function f(x) = 5 (2x + 1) - x+ x2 + 1 ANTIDERIVATIVE :…

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Q: where the populations x(t) and y(t) are measured in thousands and t in years. Use a numerical solver…

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Q: 2. Consider an explosion-versus-extinction population model of the form dr =r(r-1)+a dt where a is a…

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Q: Calculate all of the critical points of the function: f(x, y) = x² + 9y² + 6 is a relative minimum

A: Given function is f(x,y)= x^2 + 9y^2 +6

Q: (1) Determine if the series are divergent or are absolutely or conditionally convergent: (2) Σ n=0…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5. Find dz/dt. (a) z = e'-ry; r = t/2,; Y = 5t (b) z = 3r2y: r = t%; y = t x = t!/2.

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