Verify the Divergence Theorem for the vector field and region: F = (7x,3z, 8y) and the region x2 + y < 1,0 < z <9 I, F dS = Wr div(F) dV =
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Q: (a) Verify the Divergence Theorem for the vector field and region: F = (5x, 6z, 5y) and the region…
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A: f = y x2 ∂f/ ∂x = 2xy g = x z4 ∂g/ ∂y = 0 h = z y3 ∂h/ ∂z = y3
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Q: Verify the Divergence Theorem for the vector field and region: F = (4x, 6z, 8y) and the region x² +…
A: Solution
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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…
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Q: diverge
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- Find the gradient vector field of f(r, y, z) = x³yª + y³z³ + cz°.Find a vector tangent to the curve of intersection of the two cyclinders z² + y² = 98 and y? + 2² = 98 at the point (-7, –7, 7). %3D O 196i+ 98j+ 196k O 196i+ 196j+ 98k O-196i + 196j + 196k O-98i+ 196j+ 196k O 147i+ 196j+ 196kCalculate vector field F = (2 · z² + 2 · x²)i + (2 · y³ + 4 · x)j + (2 · x² · z³ + 2)k . a flux from a box with the coordinates of opposite corners (1,0,0) and (2,1,1) and you will be parallel to the coordinate planes. Use Gaussian divergence theorem fF.dS = SSS V · FdV. PM
- Find all the integral curves of the vector fields, indicate the domains of each vector field, and obtain two integral surfaces in each case (a) V = (y,-3,0), (b) V = (1, y, ry(22 + 1)). %3D %3DVerify the Divergence Theorem for the vector field and region: F = (4x, 6z, 8y) and the region x² + y² < 1,0 < z< 4 l F. ds = SIR div(F) dV =Find curl F for the vector field at the point (9, -9, 5). F(x,y,z) = x²zi - 2xzj + yzk curl F