QUESTION 5 4 Let F(r, y, 2) = ai +uj + zk and o be the portion of the surface z = 8T – x2 – y² that lies above the xy- plane. Suppose that o is oriented outward. (C) Evaluate the surface integral ff,F·n dS i. directly ii. using Divergence Theorem (c) What can you conclude from the answer in parts (c) i. and ii.? (d) Describe the circumstances when Divergence Theorem cannot be applied.

Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3…

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Q: Consider the surface z = (x + 1)² + (y – 2)² – 1 - Select an equation of the tangent plane to the…

A: we have to find the equation of the tangent plane of the surface 2=(x+1)2+(y-2)2-1 atthe point…

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²- 25 Let F(x, y, z) = 1² + 2xy + y² + 2². (a)…

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Q: B Suppose we want to find all the points on the surface gx, y) x+ 4y - 4 where the tangent plane is…

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Q: 5. Consider the surface S of equation 1-2 - y² An equation for the line tangent to the surface S at…

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Q: Consider the equation of the surface S given by -2X“ - yPz° + xy = -4, where a is an odd number and…

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Q: Advanced Math 4. Let f: S^2 → S^2 be a reflection of the sphere which leaves the plane H = {(x, y,…

A: Given Plane : H =x,y,z100x +239x+11z=0 To find: All great circles which are invariant under f.

Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Find a parametric representation of the surface in terms of parameters u = x and v = y. NOTE: Enter…

A: a) z+zx2-6y=0b) y2-10z=11

Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Find g, (0,3). ) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3…

A: 1st option is correct

Q: Q3] (A) Verify Stokes' theorem where Ã= (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z =…

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Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: Consider the surface given by the parametric vector function (image)   1. The graph of r (u, v) is…

A: Given : a surface given by the parametric vector function ru, v=sinucosvi→+sinusinvj→+sin2ucosvk→…

Q: Find parametric equations for the surface obtained by rotating the curve y = eX, 0 sx 5 4, about the…

A: Consider the curve y=e-x,    0≤x≤4 Recollect: The parametric equations of the surface obtained by…

Q: The parametric representation of the surface x² – 6x + z² = 0,0 < y < 2 %3D is a) (u, v) = (3 cos u…

A: The general form of the parametric equation of the surface in three-dimensional space is given by…

Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: #10 For the surface x³-2xz+y4+1=xy do: (a) Find the tangent plane at point (1,1,1),, Find…

A: (a) Equation of tangent plane at point (1,1,1) is: y=1(b) Equation of normal line at the point…

Q: Find all points on the curve e = {{r,y) : x² – ry + y? = 7} where the tangent line to C is…

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Q: Calculate Tu, Tu, and n(u, v) for the parametrized surface at the given point. Then find the…

A: NOTE: Refresh your page if you can't see any equations. . here we have u=5 and v=9 so the point…