Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine a, b, and c from the three equations given at the three data points first and then carry out the integration over the two slices with the quadratic curve being the integrand.

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A: Answer

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Q: Optimize the function f(x,y) = x^2+y^2 given the condition of x=y^2-5.

A: Answers are following in explanation step.Explanation:

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A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

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A: Data was collected from twenty-two mountain ash trees of different sizes. A graph of the data values…

Q: Which derivative rule is used to derive the Integration by Parts formula?

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A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…

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Q: Solve for the general solution: 6 D^3 - 13 D^2 + 6 D = 0. O y = cle^x + c2e^(2/3 x) + c3 e^(3/2 x) O…

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Q: When is integrating using the tabular method useful?

A: When is integrating using the tabular method useful?

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

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Q: Given h(x,y) = 2x^3 + 2y^3 - 9x^2 + 3y^2 -12y. Find the four critical points.

A: We have to find the critical points.

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Q: solve the ODE : xydx + ( x^2 + y^2 + 1 ) dy = 0

A: Solution: The objective is to find the general solution of the given differential equation

Q: Given the 3 functions. F(x,y) = 2x+y. G(x,y) = x^2 + y, and H(x,y) = (x^3 + y^3) / (x^2 + y^2)…

A: Given: Fx,y=2x+y, Gx,y=x2+y, Hx,y=x3+y3x2+y2To classify each of the above given function as linear,…

Q: Task 2: Find the point on the curve y = x^2 closest to the point (0, 15)

A: answer is in next step