Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 67: 42


$\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}=-5$

Work Step by Step

$\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}$ Take out common factor $x^{2}$ in the numerator and simplify: $\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}=\lim\limits_{x \to 0}\dfrac{x^{2}(x^{2}-5)}{x^{2}}=\lim\limits_{x \to 0}x^{2}-5=...$ Apply direct substitution to evaluate the limit: $\lim\limits_{x \to 0}x^{2}-5=(0)^{2}-5=-5$
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