Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises: 18

Answer

$\textbf{r}'(\pi) = \langle -2, 0, 0\rangle$

Work Step by Step

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle 2sin(t),3cos(t),sin(t/2)\rangle$ $\textbf{r}'(t) = \langle 2cos(t), -3sin(t), 0.5cos(t/2)\rangle$ $\textbf{r}'(\pi) = \langle 2cos(\pi), -3sin(\pi), 0.5cos(\pi/2\rangle = \langle -2, 0, 0\rangle$
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