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: 25

Answer

$-1$

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: $\lim _{x\rightarrow 0}\dfrac {x^{2}-4}{x^{2}+4} \\=\dfrac {\lim _{x\rightarrow 0}\left( x^{2}-4\right) }{\lim _{x\rightarrow 0}\left( x^{2}+4\right) } \\=\dfrac {0-4}{0+4} \\=-1$
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