Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.1 Limits, Rates of Change, and Tangent Lines - Exercises - Page 44: 2


29.4 m/s

Work Step by Step

Instantaneous velocity=$\lim\limits_{\Delta t \to 0}$(average velocity) $=\lim\limits_{\Delta t \to 0}\frac{\Delta s}{\Delta t}$ For the time interval [3, 3.1], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.1)^{2}-4.9(3)^{2}}{3.1-3}=29.89$ For the time interval [3, 3.01], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.01)^{2}-4.9(3)^{2}}{3.01-3}=29.449$ For the time interval [3, 3.0001], $\frac{\Delta s}{\Delta t}=\frac{4.9(3.0001)^{2}-4.9(3)^{2}}{3.0001-3}=29.40049$ We see that as $\Delta t$ tends to 0, $\frac{\Delta s}{\Delta t}$ tends to 29.4. That is, at t=3, $\lim\limits_{\Delta t \to 0}\frac{\Delta s}{\Delta t}=29.4\,m/s$
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