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 - 14.5 Motion in 3-Space - Exercises - Page 744: 4



Work Step by Step

Since $r(t)=\lt 0,e^t, -\cos(2t)\gt$, then the velocity vector is given by $$r'(t)=\lt 0,e^t, 2\sin(2t)\gt$$ and the acceleration vector is given by $$r''(t)=\lt 0,e^t, 4\cos(2t)\gt.$$ Moreover, the speed at $t=0$ is $$v(0)=\|r'(0)\|=\sqrt{0+1+0}=1.$$
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