Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Review - True-False Quiz - Page 881: 11



Work Step by Step

Given; $|r(t)|=1$ for all the values of $t$ $1$ can be written as; $Sin^{2}t+cos^{2}t=1$ Let us suppose our function as $r(t)=(Sin(t^{2}),cos(t^{2}),0)$ Then $r'(t)=(2tcost, -2t sint,0)$ $|r'(t)|=\sqrt{4t^{2}. cos^{2}t+4t^{2} sin^{2}t}$ $=2t(1)$ Thus, $|r'(t)|=2t$ which is not a constant. Hence, the given statement is false.
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