## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 31

#### Answer

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

#### 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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