University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.2 - Limit of a Function and Limit Laws - Exercises - Page 68: 73

Answer

$$\lim_{\theta\to0}g(\theta)=1$$

Work Step by Step

$$g(\theta)=\frac{\sin\theta}{\theta}$$ (a) The table is shown below. As we can see from 2 tables below, as $\theta$ gets more decimals and approaches $0$, the value of $g(\theta)$ also gets more decimals and apparently approaches $1$. So I would estimate here that $\lim_{\theta\to0}g(\theta)=1$. (b) The graph is shown below. Again, looking at the graph, the closer $\theta$ approaches $0$, the closer $g(\theta)$ gets to $1$.
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