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 709: 8


The curve intersects the x-axis when $ t=3$.

Work Step by Step

The space curve given by $$ r(t) = \langle t^2, t^2-2t-3, t-3 \rangle $$ intersects the x-axis when $ y=0, z=0$; that is, we have $$ t^2-2t-3=0, \quad t-3=0\Longrightarrow t=3.$$ Hence, the curve intersects the x-axis when $ t=3$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.