Suppose the control problem is 10 Maximize(y +4u)dt Subject to y' = 2y + u and y(0) = 10, y(10) free, u(t) = [0, 10] The Hamiltonian function will be given by

Q: Q2: If D = d dt > find a complete solution of: (D+2)x+ (D+4)y = 1 (D+1)x+ (D+5)y = 2

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Q: fa(4, 3) = 2, fy(4, 3) = -6, 6. dz find at t = 2 when x = g(t), y = h(t) and dt g(2) = 4, g'(2) = 2.…

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Q: (1,2) 6. Evaluate 0,1 (x²-y) dx + (y² +x) dy along a straight line from (0,1) to (1,1) and then from…

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Q: t²y' + 2ty - y³ = 0

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Q: If ƒ(x) = f (t³ + 5t² + 7) dt then ƒ"(x): =

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Q: If f(x) = S5 (t³ + 7t² + 3) dt then f"(2) =O

A: To find the second order derivative , we first invoke the fundamental theorem of calculus , which…

Q: ds/dt if s=(t9+6)(t8-6)

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Q: Question 2 Differentiate y = In(3x – 2x). %3D - 12z3-2 O y'= |3D 3z4-2r 12x – 2 |3D dz 3z4-2z 1 O y'…

A: Explanation of the answer is as follows

Q: Determine the critical (equilibrium) points. dy = 3?(2 – 3²), –0∞ < yo < ∞ dt (y, f(y)) (,) =| (y,…

A: To find critical points we have to solve equation f(y)=0 as

Q: find a real root of the equation x-4x-9 0

A: Let f(x)=x3-4x-9 Substitute x=1,2,3 one by one in the function to obtain the corresponding values of…

Q: 2) For what value of c does y = cx + have a relative minimum at x = 2? ? (A) ³/ (B) (C) 0 (D) 2

A: Given Function is as follows For Relative minimum,

Q: Suppose the control problem is Maximize [(y-²)dt 0 Subject to y'=u and y(0) 10, y(1) = a = The…

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Q: Suppose the control problem is The Hamiltonian function will be given by [² (2y + 3u)dt Subject to…

A: As per the question we are given a optimal control problem. Where we are given the cost function and…

Q: 2. Explain why the system f x' {y'. 9 1 + f² + g² 1 + f² + g² trajectories as x' = f(x, y). y' =…

A: The given system of differential equations is: x'=f1+f2+g2y'=g1+f2+g2 The objective of the question…

Q: If L(x, y, y/) = y² (1+ (y/)²)³ what are Ly and Ly? O Ly = 2y(1+ (y)²)³ and Ly = 6y"y² (1+ (y')²)² O…

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Q: 3 L[y] =y' --y is a linear operator. If u(x) = −4x² + 2x, then find L[u(x)]. X a) -4x² - 6x b) -…

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Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: DE dx dt = x² - 4x + 3. (a) Its stable critical point is X = unstable critical point is X =

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Q: 10. Use the second derivative test to classify the critical point(s) of the function ƒ (x, y) = x³ —…

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Q: 21. If F(x)= [ VP +1 dr, then F'(2) = %3D (A) -3 (В) -2 (C) 2 (D) 3 (E) 18

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Q: [y = = V +2 u?-1] 3 Vx2 + 2 u2+1.

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