Use the divergence theorem to compute the value of flux integral F. dS, where F(x, y, z) = 5yj - 5zk and S consists of the union of paraboloid y = x2 + z?, 0 sys 1, and disk x² + z? s 1, y = 1, oriented outward. What is the flux through just the paraboloid?

Q: a) Compute the surface area of the portion of the plane x+y=z = 0 contained inside the cylinder x² +…

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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: Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation…

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Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

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…

Q: Let F= (xz, yz, 1) and D = {(x, y, z); x² + y² + z² ≤ 25, z ≥ 3} . Calculate the flux of F outwards…

A: The flux of a vector field F=(f1(x,y,z),f2(x,y,z),f3(x,y,z)) outwards across D can be calculated…

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…

Q: Find the flux of the vector field F(x, y, z) = [xy, yz, zx] through the cylinder x2+y2 <= 1, 0 <= z…

A: The given problem is to find the flux of the vector field through the given surface of the cylinder…

Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: Let C be the circle centered at the origin with radius 4 oriented clockwise, and let F(x, y) = (2x +…

A: Given: The vector field across the circle C centered at the origin with radius 4 oriented clockwise…

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 Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: Use Divergence theorem to find the outward flux of F = (7x², et², cos³ (y² + x)) of the cube in R³…

A: Given that  and the cube  bounded by the planes The Divergence Theorem

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 the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

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Q: Let v = (x²z, 5 — 4xyz, xz²) be the velocity field of a fluid. Compute the flux of v across the…

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Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The vector field is F=xi^+yj^+zk^. The curves surface is x2+y2=1 bounded below by the plane x+y+z=2…

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Let C' be the circle centered at the origin with radius 3 oriented clockwise, and let F(x, y) = (−7x…

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Q: Find the outward flux of the vector field F (x, y, z) = x³i + y³j+(z³ + xz)k across the surface of…

A: The vector field given is as follows: Fx, y, z=x3i^+y3j^+z3+xzk^ We are asked to find the outward…

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: Find the flux of the field F(x, y, z) = (x, y, -2z) through the surface z = ! =1– 2² – y² (0 < ¤< 1,…

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Q: Find the flux S S;F · dS of the constant vector field F(x, y, z) = (0,0, 1) across the surface S…

A: Let F be a constant vector field over a surface S given as  F(x,y,z)=0,0,1  The surface S is…

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

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Q: 1. Find a vector valued function that represents the curve of intersection of the semi-ellipsoid x²…

A: The equation of the semi-ellipsoid is The cylinder is

Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

Q: Use the Divergence Theorem to find the flux of F = (xy², x²y, y) outward through

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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: Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane…

A: We have to find the flux F(x,y,z)=2xi+2yj+zk across the point of the paraboloid z=4-x2-y2 above the…

Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

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: 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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