Show that the tangent at any point of the curve whose equations referred to rectangular axes are x = 3t, y = 3t², makes a constant angle with the line y = z- x = 0 z = 2t³

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Q: RECURRENCE FORMULA: an+2 = n 0 1 2 23 3 4 5 -2(n+1)an+1+nan+4an (n+1)(n+2) an ao a1 a2 = -a1 az = ay…

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Q: Runge Kutta 2nd Order? Runge Kutta 4th Order? dy dx y (0) = 2 y(4) = 75.3386 = 4e0.8x-0.5y

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Q: Please help for the local max

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Q: 8. Solve 2y"+y' = g(t); g(t) = (4t; t < 1, 16;t ≥ 1:y(0)=-6, y'(0)=1

A: Sol:- First write g(t) in terms of unit step function :- gt=4tt&lt;16t≥1gt=4t*Ht-Ht-1+6Ht-1Now , we…