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 - 14.3 Arc Length and Speed - Exercises - Page 725: 12



Work Step by Step

We have $r'(t) =\lt 1, 2 t, 3t^2\gt$. Hence the speed $v(t)$ is given by $$v(t)=\|r'(t)\|=\sqrt{1+4t^2+9t^4} . $$ At $t=1$, $v(1)=\sqrt{14}$
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