Use the Divergence Theorem to calculate the surface integral      S F · dS;  that is, calculate the flux of F across S. F(x, y, z) = x4i − x3z2j + 4xy2zk, S is the surface of the solid bounded by the cylinder  x2 + y2 = 4  and the planes  z = x + 3 and z = 0.

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A: The weight of the child is 42 lbs The weight of the child in kilograms is 42×0.4536=19.0512≈19…

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

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Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

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Q: Let F(x, y) = 2x 2yi + 3xyj, and C be the boundary of the square with corner points (±1, ±1),…

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Q: (iv) and (0, -1) to (1, 1). Find the circulation of F round the curve C, where F=e* siny i + e*…

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

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Q: Let F(x, y) = 2x 2yi + 3xyj, and C be the boundary of the square with corner points (±1, ±1),…

A: The objective of this question is to find the flux of the vector field F across the boundary C of…

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Q: f(x,y,z) = x e Yz. a) Find Vf = Type an exact answer, using radicals as needed.) b) Determine the…

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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: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

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

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Q: Use a parameterization to find the flux SF-n do of F=2²i+xj-3zk in the outward direction (normal…

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Q: 4. Let F(r, y, z) =-ri+ yj + zk and o be the portion of the surface z = 8x-² - y? that lies above…

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Q: Compute the surface integral of the function f(x, y, z) = 2xy over the portion of the plane 2x + 3y…

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Q: Find the flux of the field F(x,y,z)=z¹ i+xj- 6z k outward through the surface cut from the parabolic…

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Q: Calculate the surface integral // y ds, where S is the part of the helicoid defined by the S vector…

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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)…

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Q: Find the flux of F= through of the total surface of the closed cone y=(x2+z2)0.5 with 0 < y < 2…

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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: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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Q: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

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