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: 29

Answer

$2$

Work Step by Step

$\lim _{x\rightarrow 2}\dfrac {x^{2}-4}{x^{2}-2x} \\=\lim _{x\rightarrow 2}\dfrac {\left( x-2\right) \left( x+2\right) }{x\left( x-2\right) }$ Cancel out the common factor: $=\lim _{x\rightarrow 2}\dfrac {x+2}{x} \\=\dfrac {2+2}{2} \\=2$
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