Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 68: 99

Answer

Please see below.

Work Step by Step

Looking at the graphs, we find that as $x$ approaches $0$, the functions $f(x)=x$ (the red graph)and $g(x)= \sin x$ (the blue graph) approach approximately the same values. So, the function $h(x)=\frac{g(x)}{f(x)}= \frac{ \sin x }{x}$ (the green graph) must approach $1$ when $x$ approaches $0$, as confirmed by the graph. Thus, we can conclude that$$\lim_{x \to 0} h(x)=1.$$
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