Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.6 Parametric Surfaces and Their Areas - 16.6 Exercises - Page 1160: 14


Plot $VI$

Work Step by Step

Given that $r(u,v)=uv^{2}i+u^{2}vj+(u^{2}-v^{2})k$ To find the grid curves corresponding to $v$ as constant , substitute $v=k$ Then $x=ukv^{2}$ and $z=(u^{2}-k^{2})$ Eliminating $u$ gives us $z=\frac{u^{2}}{k^{4}}-k^{2}$ This is a parabola parallel to $xz$ plane, only plot$VI$ contains parabolic grid curves.
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