Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 18


$$\sqrt{10 } $$

Work Step by Step

Since speed is given by \begin{align*} \frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\ &=\sqrt{ \frac{4t^2}{(t^2+1)^2}+9t^4 } \end{align*} Then \begin{align*} \frac{d s}{d t}\bigg|_{t=1} &=\sqrt{ \frac{4 }{(2)^2}+9 } \\ &=\sqrt{10 } \end{align*}
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