Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Exercises - Page 167: 9


$$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}=\infty$$

Work Step by Step

$$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}$$ As $r\to 9$, $\frac{\sqrt r}{(r-9)^4}$ approaches $\frac{\sqrt9}{(9-9)^4}=\frac{3}{0}=\infty$ Therefore, $$\lim\limits_{r\to9}\frac{\sqrt r}{(r-9)^4}=\infty$$ *NOTE: In this situation, since we cannot simplify the denominator so that it would not be 0 when we plug in the number, we must accept the fact that this function would approach infinity as $r\to9$.
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