Let S be the closed surface that bounds the region enclosed by the plane z = 4 and the circular paraboloid z = x² + y2, and let F(x, y, z)=-3xi - 3yj - 4zk. Verify the divergence theorem by calculating the outward flux of F through S, both as a surface integral and as a triple integral. Show all work clearly on your paper. No need to type anything here.

Q: Determine the flux of F(x, y, z) = across the surface with an upward orientation. Let the surface…

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Q: Verify Stokes' theorem where A = (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z=2-√√x² + y²…

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Q: Calculate the flow of F(x, y, z) = (y², x, x²) across the surface z = 4-x²-y² above the z = 1 plane

A: The field is F→(x, y, z) = y2, x, x2. The surface is . Then fx, y, z=z+x2+y2-4 Obtain the normal:…

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: Let z = g(x, y) = f(3 cos(ry), y + ev) provided that f(3, 6) = 4, fi(3, 6) = 2, f2(3, 6) = 3. %3D i)…

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Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

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Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: b) Given F(.r, y. :) = (r + cosh 2)i+ (2y-3r*y)j-(r + 4y*:) k. Use Gauss's theorem to calculate F.n…

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Q: Let z = 9(x, y) = f(3 cos(xy), y + e™y) provided that f(3,7) = 4, fi (3, 7) = 2, f2(3, 7) = 3. i)…

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Q: A normal vector to the tangent plane for the surface z = , at the point (1, 1, 1) is: y - Select…

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Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

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Q: tz = g(x, y) = f(3 cos(xy), y + e#") provided that f(3, 7) = 4, f1(3, 7) = 2, (3, 7) = 3. %3D Find…

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Q: F.N= (b) Calculate the normal component of F to the surface at P = (1, 2, 9) = (2, 3). (Use symbolic…

A: Given:It is given that  and  is the oriented surface parameterized by  for  and .To Find:(a) We have…

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: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

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Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

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Q: Let z = g(x, y) = f(3 cos(xy), y+ e#y) provided that f(3,6) = 6, f1(3, 6) = 2, f2(3, 6) = 5. i) Find…

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Q: c) Use Stokes' theorem to evaluate where F(x, y, z) = (x²+y²z) i+(x²+xy²) j+(x²+z²) k, and C is…

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Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: 2. Consider the surface defined by Let F(x, y, z) = cos(x) + е¹² + yz. (a) Evaluate F(0,1,2). xz…

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Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

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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: (1) Let F(r, y, z) = (y², e², z). (a) Compute the divergence of F. (b) Use the divergence theorem to…

A: Answer

Q: x² - y²-2²-4x - 2z+3=0

A: The given surface is x2-y2-z2-4x-2z+3=0T is the trace of S using x=2.To find the two cordinate when…

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Use Stokes' theorem to evaluate where = 3x²1+8x³yj + 3x²yk (V x F) - dA and S is the portion of the…

A: Given that S is the portion of the  plane that lies inside the box defined by the .

Q: Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the…

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Q: i) Find g1 (0, 4). ii) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z…

A: Since g(x, y) = f(3cosxy,y+exy)