Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 17 - Line and Surface Integrals - Chapter Review Exercises - Page 970: 12

Answer

$div\left( {\bf{F}} \right) = {{\rm{e}}^{x + y}} + {{\rm{e}}^{y + z}} + xy$ $curl\left( {\bf{F}} \right) = \left( {xz - {{\rm{e}}^{y + z}}} \right){\bf{i}} - yz{\bf{j}} - {{\rm{e}}^{x + y}}{\bf{k}}$

Work Step by Step

We have ${\bf{F}} = \left( {{F_1},{F_2},{F_3}} \right) = \left( {{{\rm{e}}^{x + y}},{{\rm{e}}^{y + z}},xyz} \right)$. 1. $div\left( {\bf{F}} \right) = \frac{{\partial {F_1}}}{{\partial x}} + \frac{{\partial {F_2}}}{{\partial y}} + \frac{{\partial {F_3}}}{{\partial z}}$ $div\left( {\bf{F}} \right) = {{\rm{e}}^{x + y}} + {{\rm{e}}^{y + z}} + xy$ 2. $curl\left( {\bf{F}} \right) = \left| {\begin{array}{*{20}{c}} {\bf{i}}&{\bf{j}}&{\bf{k}}\\ {\frac{\partial }{{\partial x}}}&{\frac{\partial }{{\partial y}}}&{\frac{\partial }{{\partial z}}}\\ {{{\rm{e}}^{x + y}}}&{{{\rm{e}}^{y + z}}}&{xyz} \end{array}} \right|$ $curl\left( {\bf{F}} \right) = \left( {xz - {{\rm{e}}^{y + z}}} \right){\bf{i}} - yz{\bf{j}} - {{\rm{e}}^{x + y}}{\bf{k}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.