Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 14 - Calculus of Vector-Valued Functions - 14.1 Vector-Valued Functions - Exercises - Page 710: 9


The curve does not intersect the XY-plane.

Work Step by Step

The space curve given by $$ r(t) = \langle t, t^3, t^2+1 \rangle $$ intersects the xy-plane when $ z=0$, that is, we have the equation $$ t^2+1=0\Longrightarrow t^2=-1$$ which has no solution in $ R $. Hence, the curve does not intersect the xy-plane.
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