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 76: 18


$\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=4$

Work Step by Step

$\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}$ Quotient: because $ \lim\limits_{x \to 1}{h(x)} = 2\ne0$ $\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=\frac{\lim\limits_{x \to 1}{f(x)}}{\lim\limits_{x \to 1}{h(x)}}$ We know that $ \lim\limits_{x \to 1}{f(x)} = 8$ $\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=\frac{\lim\limits_{x \to 1}{f(x)}}{\lim\limits_{x \to 1}{h(x)}}=\frac{8}{2}=4$ So $\lim\limits_{x \to 1}{(4f(x))}=4\lim\limits_{x \to 1}{f(x)} = 4\times8=32$
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