Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.3 Techniques for Computing Limits - 2.3 Exercises - Page 77: 52

Answer

$3a^2$

Work Step by Step

We have to determine $L=\lim\limits_{x \to a}\dfrac{x^3-a^3}{x-a}$. Factor the numerator using the identity: $x^3-y^3=(x-y)(x^2+xy+y^2)$: $L=\lim\limits_{x \to a}\dfrac{(x-a)(x^2+ax+a^2)}{x-a}$ Simplify: $L=\lim\limits_{x \to a} (x^2+ax+a^2) Determine $L$: $L=a^2+a^2+a^2=3a^2$
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