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c) Find the flux of the vector field F(x, y, z) = 4xi + 4yj + 2k outward (normal away from the z-axis) through the surface cut from from the bottom of the paraboloid z = dz= x² + y²2 by the plane z = 1. Use both a parametrization and an implicit representation of the surface and check that the results agree.

c) Find the flux of the vector field F(x, y, z) = 4xi + 4yj + 2k outward (normal away from the z-axis) through the surface cut from from the bottom of the paraboloid z = dz= x² + y²2 by the plane z = 1. Use both a parametrization and an implicit representation of the surface and check that the results agree.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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c) Find the flux of the vector field F(x, y, z) = 4xi + 4yj + 2k outward (normal away from dz= x² + y² the z-axis) through the surface cut from from the bottom of the paraboloid z = by the plane z = 1. Use both a parametrization and an implicit representation of the surface and check that the results agree.
Transcribed Image Text:c) Find the flux of the vector field F(x, y, z) = 4xi + 4yj + 2k outward (normal away from dz= x² + y² the z-axis) through the surface cut from from the bottom of the paraboloid z = by the plane z = 1. Use both a parametrization and an implicit representation of the surface and check that the results agree.
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