(a) Use the divergence theorem to evaluate the flux of the vector field F(x, y, z) = 0i + 4xj-2 z k across the surface S, where S is the closed cylinder bounded by the surface y + x² = 1, and the planes z = 0 and z = 4. (b) Calculate the flux of the same vector field F(x, y, z) = 0i+ 4 xj-2 z k through C, the open curved cylindrical surface bounded by y + x² = 1, z = 0 and z = 4. Use the result from part (a) and subtract the contributions from the top and bottom flat "lids".

Q: Use the divergence theorem to find the outward flux of the vector field F(x, y, z) = 4x²i + 5y²j +…

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Q: a) Let F. 2x³ +Y;+2 cosz+X+23³ k +2005 3 j+ -k be the vector field. Use the Divergence Theorem to…

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Q: In Exercises 5-9 compute the flux of the vector field F through the parameterized surface S. -F = yi…

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Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

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Q: Compute the flux of the vector field F(x, y, z) = 5i + 5j+ 6k through the rectangular region with…

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Q: 3. Consider the vector field F = (y, -x, x² + y?). Find the flux of F through S if: 9– x2 – y? above…

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Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

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Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

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Q: Use the divergence theorem to find the outward flux F ndS of the vector field F = cos(8y + 8z) i + 4…

A: …

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Use the divergence theorem to find the outward flux    ∫     ∫ SF · n dS   of the vector field F  =…

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Q: 10. [ Find the flux of the vector field F(x, y, z)= 3 over the surface S, where S is the surface of…

A: The general form of a vector-valued function in three dimensions is given by F→=Fx, Fy, Fz, where…

Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x^2…

A: The function given to us is F→=-3x2+2xz-y, 7y3-6y, 9x2+4z2-3x. We are asked to find the total flux…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = xy2i + yz2j +…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

A: Given The given vector field is F=3z+x,7x-9y,y+5z Region between the spheres of radius 1 and 4.

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2,…

A: The vector field is given as

Q: Find the counterclockwise circulation and outward flux of the field F = xyi + y2j around and over…

A: Theorem used:

Q: Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the…

A: Solution; Consider the given function: F(x, y) = xy, x-y = P, Q P = x y Q = x -y and the boundaries…

Q: For the vector field: F = (x + y)i + (y + z)j + (z + x)k 1) Compute the flux out of the cube bounded…

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Q: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

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Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

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Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…

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Q: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

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Q: Q5. Consider the vector field F(x, y, z)=xi + 2yj + (x² + 4y²) k and the closed surface S made up of…

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Q: 4. (a) Show that the outward flux of the postion vector field F(x,y,z) = (x)7+ (y)] + (z) through a…

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Q: Let E be the solid region bounded by the upper half-sphere x² + y? + z2 = 4 and the plane z = 0. Use…

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Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

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A: theory: graph:

Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

Q: Find the divergence of the vector field F(x, y, z) = In(x² + y? )i+xyj+ln(y² + 2²)k. 2x 2z +x + x2 +…

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Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: 7. Using the divergence theorem compute the outward flux of the vector field F(x, y, z) = x°i+…

A: step:-1 Divergence Theorem:-  ∬F.ndS=∭divF dV=∭divF  ρ2 sinϕ dρ dθ dϕ  Given that  F→=x3i…

Q: 21. Compute the flow of the vector field F = r through the surface of the ellipsoid y² + 2 = 1 in…

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Q: Jse the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z) D is…

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Q: Find the flux of the vector field F = xi - 3y j - 2z k through the part of the plane 2.x + 3y + z =…

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Q: Why does a two-dimensional vector field with zero divergence on a region have zero outward flux…

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Q: Problem #4: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

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Q: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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Q: (b) Let Q be the region bounded by the graphs of x² + y² = 4,z = 0 and z = 1. Let S denote the…

A: Let's find.

Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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Q: 9) ca) 9 Consider the outward flux of vector field F (x,y,Z)= yt+ xyĵ+ zk across the surfaces…

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