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 - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 33


$$ L(s)= \langle 2,0, -\frac{1}{3}\rangle +s \langle-1,0,\frac{1}{2}\rangle .$$

Work Step by Step

Since we can write $ r (s)=\langle 4s^{-1},0, -\frac{8}{3}s^{-3}\rangle, $ then we have the derivative vector $ r' (s)=\langle -4s^{-2},0,8s^{-4} \rangle $ Then, the parametrization of the tangent line at $ s=2$ is given by $$ L(s)=r (2)+sr'(2)=\langle 2,0, -\frac{1}{3}\rangle +s \langle-1,0,\frac{1}{2}\rangle .$$
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.