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 - Page 884: 26


$=\dfrac {5}{3}$

Work Step by Step

Recall: (1) $\lim _{x\rightarrow c}\dfrac {f\left( x\right) }{g\left( x\right) }=\dfrac {\lim _{x\rightarrow c}f\left( x\right) }{\lim _{x\rightarrow c}g\left( x\right) }$ (2) $\lim _{x\rightarrow c}f(x) = f(c)$ Use the rules above to have: $\Rightarrow \lim _{x\rightarrow 2}\dfrac {3x+4}{x^{2}+x} \\=\dfrac {\lim _{x\rightarrow 2}\left( 3x+4\right) }{\lim _{x\rightarrow 2}\left( x^{2}+x\right) } \\=\dfrac {3\times 2+4}{2^{2}+2} \\=\dfrac {10}{6} \\=\dfrac {5}{3}$
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