Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x − z i + y − x j + z − y k ; σ is the surface of the cylindrical solid bounded by x 2 + y 2 = a 2 , z = 0 , and z = 1 .
Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x − z i + y − x j + z − y k ; σ is the surface of the cylindrical solid bounded by x 2 + y 2 = a 2 , z = 0 , and z = 1 .
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.
Use the Divergence Theorem to find the flux of
F(x, y, z)=z³ i-x³j+y³ k
across the sphere x² + y² + z² = a² with outward orientation.
$ = i
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)
University Calculus: Early Transcendentals (3rd Edition)
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