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: 16


plot $V$

Work Step by Step

Given : $x=(1-u)(3+cosv)cos4\pi u$ $y=(1-u)(3+cosv)sin 4\pi u$ $z=3u+(1-u)sinv$ To find the grid curves corresponding to $u$ as constant , substitute $v=k$ $x=(1-u)(3+cosk)cos4\pi u$ $y=(1-u)(3+cosk)sin 4\pi u$ $z=3u+(1-u)sink$ This is an equation of helix with a non- constant radius $=k$ Only plot $IV$ and $V$ contain grid curves which are helix. But only plot $V$ contains helical grid curves with non-constant radius.
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