3. Evaluate the flux integral √ √ ·Ñds where Ễ = 2zî – 4xĵ + k for the surface S: z = 12-3x-4y in the first octant. - 4. Use the divergence theorem to evaluate √ √Ẻ · Ñds for F(x, y, z) = (2xy − 1)î + (3yz + 2)ĵ + xzk for the closed surface bounded by the cylinder x² + y² = 4, z = 4, and the coordinate planes.
3. Evaluate the flux integral √ √ ·Ñds where Ễ = 2zî – 4xĵ + k for the surface S: z = 12-3x-4y in the first octant. - 4. Use the divergence theorem to evaluate √ √Ẻ · Ñds for F(x, y, z) = (2xy − 1)î + (3yz + 2)ĵ + xzk for the closed surface bounded by the cylinder x² + y² = 4, z = 4, and the coordinate planes.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 27E
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I need help with this problem and an explanation for the solution described below. (Calculus 3):
Transcribed Image Text:3. Evaluate the flux integral √ √ ·Ñds where Ễ = 2zî – 4xĵ + k for the surface
S: z = 12-3x-4y in the first octant.
-
4. Use the divergence theorem to evaluate √ √Ẻ · Ñds for F(x, y, z) = (2xy − 1)î +
(3yz + 2)ĵ + xzk for the closed surface bounded by the cylinder x² + y² = 4, z = 4, and the
coordinate planes.
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