Answer
L’Hôpital’s Rule does not apply.
Work Step by Step
Since we have
$$
\lim _{x \rightarrow 9} \frac{x^{1/2}+x-6}{x^{3/2}-27}=\frac{3+9-6}{27-27}=\frac{6}{0}=\infty
$$
then L’Hôpital’s Rule does not apply.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.7 L'Hôpital's Rule - Exercises - Page 366: 5
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