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: 21



Work Step by Step

$\lim_{x\to1}\dfrac{f(x)g(x)}{h(x)}$ It is known that $\lim_{x\to1}f(x)=8$ $,$ $\lim_{x\to1}g(x)=3$ and $\lim_{x\to1}h(x)=2$ Evaluate the limit using the limit laws: $\lim_{x\to1}\dfrac{f(x)g(x)}{h(x)}=...$ If the limit of the denominator is different from $0$, then the limit of a quotient is the quotient of the limits of the numerator and the denominator: $...=\dfrac{\lim_{x\to1}f(x)g(x)}{\lim_{x\to1}h(x)}=...$ The limit of a product is the product of the limits of the factors: $...=\dfrac{[\lim_{x\to1}f(x)][\lim_{x\to1}g(x)]}{\lim_{x\to1}h(x)}=...$ The limits indicated are known. Substitute them into the expression and evaluate: $...=\dfrac{(8)(3)}{2}=(4)(3)=12$
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