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: 31


$$ L(t)= \langle-3,10,16 \rangle +t \langle-4,5,24 \rangle .$$

Work Step by Step

Since $ r (t)=\langle1-t^2,5t,2t^3 \rangle, $ then $ r' (t)=\langle-2t,5,6t^2 \rangle $ then, the parametrization of the tangent line at $ t=2$ is given by $$ L(t)=r (2)+tr'(2)=\langle-3,10,16 \rangle +t \langle-4,5,24 \rangle .$$
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