Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 4

Answer

$$\lim _{\theta \rightarrow 0} f(\theta)=-0.16\bar{6}=-\frac{1}{6} $$

Work Step by Step

Given $$f(\theta)=\frac{\sin \theta-\theta}{\theta^{3}}$$ Since \begin{array}{|c|c|c|c|c|} \hline \theta & \pm0.002 & \pm0.0001 & \pm0.00005 & \pm0.00001 \\ \hline f(\theta) & -0.166666633 & -0.166666661 & -0.166666648 & -0.166667285 \\ \hline \end{array} Then $$\lim _{\theta \rightarrow 0} f(\theta)=-0.16\bar{6}=-\frac{1}{6} $$
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