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: 23


Graph (V)

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 $x= t , y=\dfrac{1}{1+t^2}, z=t^2$ Here, the parametric equation for $z=t^2$ can be re-arranged as: $z=x^2$ This implies that the projection of the curve on the $xz$ plane is a parabola and the $y$ and $z$ coordinates must never be negative. This conclusion signifies the conditions indicated in the Graph{(V)
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