Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding: 23

Answer

$3$

Work Step by Step

Note that, if $f(x) \ge 0$, $\lim _{x\rightarrow c}\sqrt {f\left( x\right) }=\sqrt {\lim _{x\rightarrow c}f\left( x\right) }$ Thus, $\lim _{x\rightarrow 1}\sqrt {5x+4} \\=\sqrt {\lim _{x\rightarrow 1}\left( 5x+4\right) }$ Since $\lim _{x\rightarrow c}f(x) = f(c)$, then $\\=\sqrt {\lim _{x\rightarrow 1}\left( 5x+4\right) } \\=\sqrt {5\times 1+4} \\=\sqrt {9} \\=3$
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