Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.4 - The Precise Definition of a Limit - 2.4 Exercises - Page 114: 42

Answer

$\lim\limits_{x \to -3} \frac{1}{(x+3)^4} = \infty$

Work Step by Step

Let $M \gt 0$ be given. Let $\delta = (\frac{1}{M})^{1/4}$ Suppose that $\vert x-(-3) \vert \lt \delta$ Then: $\vert \frac{1}{(x+3)^4}\vert \gt \vert \frac{1}{\delta^4} \vert = \vert \frac{1}{1/M} \vert = M$ Therefore, $\lim\limits_{x \to -3} \frac{1}{(x+3)^4} = \infty$
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