Let S denote the part of the surface z-2 (r-1)2+(y-3)2 contained 1. within the cylinder r? + y? = 1. Parameterize the surface S in terms of coordinates u, and v. Then set up a double integral (in u and v coordinates) to evaluate the flux of F(x, y, z) = (x, y", 2) through S. For the flux integral, use the normal whose z component is negative.

Q: Consider the surface xyz = 20. A. Find the unit normal vector to the surface at the point (5, 2, 2)…

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Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

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A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

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Q: 2. Find an equation of the plane through the point (1,3,2) and perpendicular to the vector (-3, 1,4)

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