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: 34


$$ L(s)= \langle 0,1,9\rangle +s \langle1,-1,9\rangle .$$

Work Step by Step

Since we can write $ r (s)=\langle \ln s, s^{-1},9s \rangle, $ then we have the derivative vector $ r' (s)=\langle s^{-1},-s^{-2},9 \rangle $. Then, the parametrization of the tangent line at $ s=1$ is given by $$ L(s)=r (1)+sr'(1)=\langle 0,1,9\rangle +s \langle1,-1,9\rangle .$$
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