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A: Given,  F(x,y)=2x^2-4x+y^2-4y+1

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Q: Q5) Solve the following using Trapezoidal rule with n=6 2 f(x) = [²xtnx. dx 0

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A: Given: The given partial differential equation 3∂u∂t+t2∂u∂x=0 with  u(x,0)=f(x),0&lt;x&lt;1.

Q: If y(#) = and z increases from 0 to 0.5 then dy = 0.5. %3D %3D 1+ *

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Q: Qi) Solve the following PDES by direct integration. 2) = 0 дх ду 3) = x?y %3D дх ду dxdy azu -2t and…

A: Solve PDE by direct integration.  According to guidelines we solve only first question.

Q: Is a solution of the diffrntish epuation 1 yy'= -X+ with y E € ]_9,GE with x € C-G,G] 2. 3)yy:…

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Q: | 8(x + 1) (2x2 + 4x – 1) dx 3/2 5.

A: For the given integral- I=∫8x+12x2+4x-132dx Let u=2x2+4x-1 Differentiating w.r.t. x to both sides-…