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 69: 89

Answer

We can guess here that $$\lim_{x\to0}\frac{1-\cos x}{x\sin x}=0.5$$
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Work Step by Step

$$\lim_{x\to0}\frac{1-\cos x}{x\sin x}$$ (a) The graph is shown below. (b) Looking at the graph, as $x\to0$, we see that $\frac{1-\cos x}{x\sin x}$ approaches as close as $0.5$. Therefore, we can guess here that $$\lim_{x\to0}\frac{1-\cos x}{x\sin x}=0.5$$
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