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: 32

Answer

$\dfrac {5}{4}$

Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow -3}\dfrac {x^{2}+x-6}{x^{2}+2x-3} \\=\lim _{x\rightarrow -3}\dfrac {\left( x+3\right) \left( x-2\right) }{\left( x+3\right) \left( x-1\right) }$ Cancel the common factors: $\\=\lim _{x\rightarrow -3}\dfrac {\left( x-2\right) }{\left( x-1\right) } \\=\dfrac {-3-2}{-3-1} \\=\dfrac {-5}{-4} \\=\dfrac {5}{4}$
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