(a) Why do you need Monte Carlo integration?  (b) Generate 5 random values from uniform (0,1) using a =6, c=1, m=40. Start with seed X0=20 and hence evaluate the Monte Carlo integration of ∫i=05 (2x)2 dx Compare the Monte Carlo integration value with actual value of this integration.

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Q: equilibrium

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A: The objective is to check some variables.

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Q: 2. (a) Why do you need Monte Carlo integration? (b) Generate 5 random values from uniform (0,1)…

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A: dydt(t) +t2 y(t) =x(t) To solve this differential equation

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Q: Solve the inhomogeneous 1st order equation U₂ - U₁ = cost U(x, 0) = 0.

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Q: * = cos(x + y), when x = 0,y = %3D dx

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Q: You have to sketch the integration of the first graph

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Q: (d) y = x/1 (e) y = e", y = e3, and x = 1 (f) u = 2" , y = 5", and x= 1

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Q: 5. Solve Equations 2x+y+z=5,3x+5y+2z=15,2x+y+4z=8 using Gauss Seidel method

A: Stape by Step solution given below.

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Q: Why does dA/dt = 0?

A: Since area is constant therefore dA/dt=0

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A: Using partial fraction, the integrand can be written as

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Q: Solve the differnetial equation: dy/dx=3/x^2-3x^2+2 with the initial conditions (1,8). show work

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Q: Finds the solution (roots) f (x)=x^3+ x-1=O using fixed point iteration process

A: To Determine :-  The solution f  x = x3 + x -1 =0 using fixed point iteration process.