3. Use the Divergence Theorem to evaluate F.dS where F = -zyi+(z – 1) j +k and S is the surface of the solid bounded by y = 4z +4:2 –1 and the plane y = 7. Note that both of the surfaces of this solid included in S.

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A: The given function is  and the surface is bounded by the curves  and .Find  as follows.Put .So, the…

Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

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A:

Q: 4. Use Stokes' Theorem to evaluate [ F• dr when z = 4-y F(x, y. 2)= xz° 7+(x+z*)7+ -x |k. Let C is…

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A:

Q: 12. Let C represent the curve of intersection between the cylinder x² + y² = 4 and the plane z = 10…

A: The plane z=10-x will cut the cylinder x2+y2=4 to give an ellipse.

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

A:

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A:

Q: b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to…

A:

Q: Find an equation of the plane tangent to the surface z = x2 + y2 at (2, 3, 13). [Hint: Consider the…

A: Note: Here, f(x,y,z) = x2 + y2 - z and the point is (2, 3, 13).

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

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Q: b) Use Gauss' theorem to evaluate RR F. ndS where F = (x² - y)i + y³z²j + (xy – y²z³)k UTM UTM and o…

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Q: 1. Let S be the portion of the surface x² + z² = 1 lying in the first octant and bounded by x = 0, y…

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Q: Calculate || F. dS where S F = (3xy?, xe², z*) S is the surface of the solid bounded by the cylinder…

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A: Solve the following