Let F (x, y, z) = < x – ye², y + xe², 8 – 2z > and G be the solid %3D | below the paraboloid % = 4 – x" – y° and above the xy-plane. Let S be the surface boundary of G, and S; and S, be the portions of S along the paraboloid and the xy-plane, respectively. (a) Find the flux of F across the upward-oriented surface S. (b) Show that F is incompressible and then use Gauss's Divergence Theorem to find the flux of F across the positively-oriented surface S. (c) Using items (a) and (b), find the flux of F across the upward-oriented surface S.

Let F (x, y, z) = < x – ye², y + xe², 8 – 2z > and G be the solid %3D | below the paraboloid % = 4 – x" – y° and above the xy-plane. Let S be the surface boundary of G, and S; and S, be the portions of S along the paraboloid and the xy-plane, respectively. (a) Find the flux of F across the upward-oriented surface S. (b) Show that F is incompressible and then use Gauss's Divergence Theorem to find the flux of F across the positively-oriented surface S. (c) Using items (a) and (b), find the flux of F across the upward-oriented surface S.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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