Calculus 8th Edition

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

Chapter 13 - Vector Functions - 13.1 Vector Functions and Space Curves - 13.1 Exercises - Page 894: 22



Work Step by Step

The parametric equations of a circle whose radius is $r$ are given as follows: $x=r \cos t ; y =r \sin t$ From the given problem, we have $x= t \cos t , y= \sin t , z=\dfrac{1}{1+t^2}$ When we look down from a upper view with the high $z$-value then, we get a circle and the parametric equation $z=\dfrac{1}{1+t^2}$ shows that $z$ is always positive. The above conclusion signifies the conditions indicated in the Graph{(VI).
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