Let F (x, y, z) = < x – ye², y + xe², 8 – 2z > and G be the solid | Let 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 | Let 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,.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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