b) Let o be the surface of the solid enclosed by the circular cylinder x²+y?=2 and planes z=0 and z=2 oriented outward. Use the divergence theorem to find the flux of vector field F across o F(x.y,z)=x³i+y³j+z°k

Q: .3 Evaluate || F · dS, where F = and S is the helicoid with vector equation r(u, v) = 0<u < 1, 0 <…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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: Find the flux of the vector field F across the surface S in the indicated direction. F = x 2y i  -…

A: To find the flux of the vector field F across the surface S. F=x2yi−zk S is the portion of the cone…

Q: of the vector field F across the surface S in the indicated direction. F = x 2y i  - z k; S is…

A: Introduction: The flux of the vector field F is given by the formula, ∮CF.ndS=∫∫∫div(F)dA

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: Let S be the part of the plane 4x +2y+z=4 which lies in the first octant, oriented upward. Find the…

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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: 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: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

A: use divergence theorem

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

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Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: Calculate the flux of the vector field F = (yz, xy, 3) through the elliptical cone S given by the…

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Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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Q: Find the flux of F = yi+2xj-3zk through the unit disk centered at (0,3,0) in the plane y=3, oriented…

A: Given F→=yi^+2xj^-3zk^ through the unit disk centered at 0,3,0 in the plane y=3 oriented towards the…

Q: ) For the scalar potential function = (x² + y² + z²)² and the velocity vector field u-(y², z, x²)…

A: Answer

Q: b) F(x,y) represents a velocity field of a fluid over a surface S defined by z= 6-3x-2y. If the…

A: The flux over the surface S in the first octant is given by the following integral: Flux=∫SF⋅ndS…

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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Q: F = 6x i  + 6y j + 7 k; S is "nose" of the paraboloid z = 2x 2 + 2y 2 cut by the plane z = 5;…

A: This is a problem of vector calculus.