Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 34

Answer

$-\infty$

Work Step by Step

$x\rightarrow 0$ means that the values of x approach 0 from either side. For any of these x, the numerator is negative (approaches $-1).$ The denominator is positive, because $x^{2}$is not negative and approaches 0, $(x+2)$ is positive and approaches +2, so their product is positive and approaches 0. So $\displaystyle \lim_{x\rightarrow 0}\frac{x-1}{x^{2}(x+2)}=-\infty$
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