Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Section 13.1 - Vector Functions and Space Curves - 13.1 Exercises - Page 854: 22



Work Step by Step

The parametric equations of a circle having radius $r$ are; $x=r \cos t ; y =r \sin t$ Here, we have $x= t \cos t , y= \sin t , z=\dfrac{1}{1+t^2}$ We see that $x$ and $y$ look like a circle when we look down from a top view with a high z-value. The parametric equation $z=\dfrac{1}{1+t^2}$ shows that $z$ is always positive. This matches with $\bf{Graph{(VI)}}$.
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