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: 74



Work Step by Step

$$G(t)=\frac{1-\cos t}{t^2}$$ (a) The table is shown below. As we can see from 2 tables below, as $t$ gets more decimals and approaches $0$, the value of $G(t)$ also gets more decimals and apparently approaches $0.5$. So I would estimate here that $\lim_{t\to0}G(t)=0.5$. (b) The graph is shown below. Again, looking at the graph, the closer $t$ approaches $0$, the closer $G(t)$ gets to $0.5$.
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