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: 31


$\dfrac {7}{6}$

Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow -3}\dfrac {x^{2}-x-12}{x^{2}-9} \\=\lim _{x\rightarrow -3}\dfrac {\left( x+3\right) \left( x-a\right) }{\left( x+3\right) \left( x-3\right) }$ Cancel the common factors: $=\lim _{x\rightarrow -3}\dfrac {\left( x-4\right) }{\left( x-3\right) } \\=\dfrac {-3-4}{-3-3} \\=\dfrac {7}{6}$
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