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: 36

Answer

$3$

Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow 2}\dfrac {x^{3}-8}{x^{2}-4} \\=\lim _{x\rightarrow 2}\dfrac {x^{3}-2^{3}}{x^{2}-2^{2}} \\=\lim _{x\rightarrow 2}\dfrac {\left( x-2\right) \left( x^{2}+2x+2^{2}\right) }{\left( x-2\right) \left( x+2\right) }$ Cancel the common factors: $\\=\lim _{x\rightarrow 2}\dfrac {\left( x^{2}+2x+4\right) }{x+2} \\=\dfrac {2^{2}+2\times 2+4}{2+2} \\=\dfrac {12}{4} \\=3$
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