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: 32


$(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$

Work Step by Step

General form of parametric equation for $r(t)= (\sin^2 t+\cos^2 t)+t^2=5$ is: $\sin^2 t+\cos^2 t=1$ We are given that the paraboloid equation $z=x^2+y^2$ $1+t^2=5$ This gives: $t^2=4$ and $ t= \pm 2$ Now, the value of $t$ for the point of intersection are; $ \lt \sin (2), \cos (2), 2 \gt; \lt \sin (-2), \cos (-2), 2 \gt$ Point of intersection: $(0.909,-0.416,2); (-0.909,-0.416,-2)$
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