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: 26


Graph (III)

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 $x= \cos^2 t , y=\sin^2 t, z=t$ When the value of $t$ increases , then the value of $x$ goes from $1$ to $0$ but the value of $y$ goes from $0$ to $1$. The value of the $x$ and $y$ are always positive an each vary from $0$ to $1$ . Further, when $t$ changes its position then the value of $x$ goes from $0$ to $1$ but the value of $y$ is from $1$ to $0$. This conclusion signifies the conditions indicated in the Graph (III).
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