Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - 3.1 Limits - 3.1 Exercises: 23

Answer

$\displaystyle \frac{1}{3}$

Work Step by Step

see: Rules for Limits Let $a, A$, and $B$ be real numbers, and let $f$ and $g$ be functions such that $\displaystyle \lim_{x\rightarrow a}f(x)=A$ and $\displaystyle \lim_{x\rightarrow a}g(x)=B$. 4. $\displaystyle \lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x\rightarrow a}g(x)}=\frac{A}{B}$ if $B\neq 0$ (The limit of a quotient is the quotient of the limits, provided the limit of the denominator is not zero.) --------------- $\displaystyle \lim_{x\rightarrow 4}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow 4}f(x)}{\lim_{x\rightarrow 4}g(x)}$ $=\displaystyle \frac{9}{27}=\frac{1}{3}$
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