Calculus (3rd Edition)

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

Chapter 2 - Limits - Chapter Review Exercises - Page 95: 65



Work Step by Step

Suppose the limits $A, B,$ and $L$ all exist and $L=1 .$ Then \begin{align*} B&=B \cdot 1=B \cdot L\\ &=\lim _{x \rightarrow a} g(x) \cdot \lim _{x \rightarrow a} \frac{f(x)}{g(x)}\\ &=\lim _{x \rightarrow a} g(x) \frac{f(x)}{g(x)}\\ &=\lim _{x \rightarrow a} f(x)\\ &=A \end{align*}
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