A vector field is given by V = (5x²+4y)į + 5y²j + (z² + 3)k, using Gauss's theorem (or Divergence theorem), find the amount of field that flows out of a cube with dimensions 0sx< 1,0

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

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Q: Calculate the divergence of the vector field F (x, y, z) = − 10 sin(2xy)i — cos(x³y)j. (Give an…

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Q: The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y,…

A: The surface H  is defined by    .The vector field  is given by   .We have to sketch the surface H.

Q: 2. Determine if the vector field, F = (2ry- 22)i+(r² + 2z)j+ (2y-2rz)k, is conserva- tive. If the…

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Q: 2. Given vector field F= (-2y, z-2x, y + z), find the work done by ♬ on a particle that moves along…

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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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: Find the divergence of the vector field V(x, y, z) = −4xi + (y + 7 cos(x))j + (9z + 4xy) k. (Give an…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: Find the gradient vector field of f. f(x, y, z) = 7√√x² + y² + z² i + j + k

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Q: Consider the square C oriented counter clockwise, with vertices (0, 0), (2, 0), (0, 2), (2, 2) and 7…

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Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+ e5xy) k. (Give an…

A: Given that V(x, y, z) = −3xi + (y + 4 cos(x)) j + (9z + e^(5xy)) k.

Q: 1) Given the vector fields F1 = x²2 and F2 = xâ+ yŷ + z2, calculate the divergence and curl of F1…

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Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+exy) k. (Give an…

A: Given that V(x, y, z) = −3xi + (y + 4 cos(x)) j + (9z + e^(5xy)) k.