find the flux Set up and evaluate a double integral for calculating the flux of the vector field F(x, y, z) = (x, y, z), through the part of the upward oriented surface z = 5(x² + y²) that lies above the disk æ² + y² ≤ 9.

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 3 + 4x + y above…

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Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: State the theorem for Surface Independence for Curl Vector Fields.

A: Stokes' Theorem Stokes’ theorem says we can calculate the flux of curl F across surface S by knowing…

Q: Verify the Divergence Theorem for the vector field F = (-2, 3, z³) on the sphere x² + y² +2²2² = 4…

A: For the vector functionto verify the divergence theorem over the sphere

Q: nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of…

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Q: Determine the flow of the vector field (image 1), through the surface S, outwards, with S being the…

A: Given :- The flow of the vector field through the surface S , outwards , with S  being the…

Q: Compute the flux of the vector field (ï³, — xy³), out of the rectangle with vertices (0,0), (4,0),…

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Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w = (x−y, x+y, 0), clearly…

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Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Compute the curl of the vector field F = (r', y³, z*). curl(F(r, y, z)) = %3D What is the curl at…

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Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: 5 Let fi R²→R be the vector field given by F (x,y)- (4,-x). A- Calculate the circulation of f when…

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Q: Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at…

A: Given,                    To find the flux of the given vector field through a disk of radius 6…

Q: Find a formula F = (F₁(x, y), F₂(x, y)) for the vector field in the plane that has the properties…

A: Answer :

Q: For the vector field (x2,0₁ - 2x² -z²), evaluate its line integral along the closed curve, made by…

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Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Find the flux of the vector field F = xi + e6xj + zk through the surface S given by that portion of…

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Q: Compute the flux of the vector field F(x, y, z) = 3i + 2j + 2k through the rectangular region with…

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Q: a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius…

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