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 - Page 137: 25



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 $\displaystyle \lim_{x\rightarrow a}g(x)=B$. 6. For any real number $k,\displaystyle \lim_{x\rightarrow a}[f(x)]^{k}=[\lim_{x\rightarrow a}f(x)]^{k}=A^{k}$, provided this limit exists. --------------- $\displaystyle \lim_{x\rightarrow 4}\sqrt{f(x)}=\lim_{x\rightarrow 4}[f(x)^{1/2}]$ $=[\displaystyle \lim_{x\rightarrow 4}f(x)]^{1/2}$ $=9^{1/2}=3$
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