Evaluate ff F.n ds where F(x, y, z) = 12xi +24j+24x²k and is that portion of the paraboloid z = x² + y² which lies above the xy-plane enclosed by the parabolas y = 1-x² and y=x²-1. The surface is oriented by downward unit normals.

Q: Find the area of the surface, which is part of the surface z = 1 + 3x + 2y2 that lies above the…

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Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: Find the area of the surface cut out from the bottom of the paraboloid z = x² + y² by the plane z =…

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Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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Q: Find the equation of the plane tangent to the surface z = 3x² + y² at (1, 1, 4).

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Q: hat is the scalar equation of the xy plane?

A: Given query is to find the scalar equation of the XY plane.

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

A: Solution :-

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: with the p-norm 「さい Is a normed lineur s pace over fiéle cary R with respect to opera tróns addition…

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Q: The domain is the entire xy-plane.

A: Domain -Domain constitutes only the values of x on which the function is defined.

Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain