13. y = 5 x², y=3-x. —

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Q: Find the volume of the region bounded by the planes 4x + 2y + 3z = 5, y = x, x = 0, z = 0.

A: 4x+2y+3z=5,y=x,x=0,z=0.0≤z≤(5−4x−2y)3z=0⇒y=5−4x2x≤y≤5−4x25−4x2=x5−4x=2xx=56

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Q: ey-x2 Let f(x, y, z) Find gradƒ(1, 1, −1) and G(x, y, z) = fyy — fxz. X

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Q: *P(zx) ulg*J

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A: y=4x, x=1 to x=3

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Q: Problem #7: Evaluate the surface integral f FdS where F(x, y, z) = xyi - y²j-9zk and S is the sphere…

A: Calculate F.dS where  F(x, y, z)  =  xyi − y2 j − 9zk  and  S is the sphere  x2 + y2 + z2  =  9…