Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 4 - Section 4.4 - Indeterminate Forms and l''Hospital''s Rule - 4.4 Exercises - Page 316: 6

Answer

$\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = -1.5$

Work Step by Step

$\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = \lim\limits_{x \to 2}\frac{1.5(x-2)}{2-x} = \frac{0}{0}$ We can use L'Hospital's Rule: $\lim\limits_{x \to 2}\frac{f'(x)}{g'(x)} = \lim\limits_{x \to 2}\frac{1.5}{-1} = -1.5$ $\lim\limits_{x \to 2}\frac{f(x)}{g(x)} = -1.5$
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