Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x i + y j + z k ; σ is the surface of the solid bounded by the paraboloid z = 1 − x 2 − y 2 and the xy -plane.
Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x i + y j + z k ; σ is the surface of the solid bounded by the paraboloid z = 1 − x 2 − y 2 and the xy -plane.
Determine the flux of F(x, y, z) = < −x2 + x, y, 8x3 − z + 9 > across the surface with an upward orientation. Let the surface be the portion of the paraboloid z = 9 − 4x2 −4y2 on the first octant above the plane z = 1. (note: do not use gauss' theorem)
Determine the flux of F(x, y, z) = < −x2 + x, y, 8x3 − z + 9 > across the surface with an upward orientation. Let the surface be the portion of the paraboloid z = 9 − 4x2 −4y2 on the first octant above the plane z = 1.
Evaluate
F.ndS for the given F and ơ.
(b) F(x, y, z) = (x² + y) i+ xyj – (2xz + y) k,
o : the surface of the plane x + y + z = 1 in the first octant
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