Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 67: 37


a) $10.$ b) $5.$ c) $6.$ d) $\dfrac{3}{2}.$

Work Step by Step

Using Theorem $1.2$: a)$\lim\limits_{x\to c}[5g(x)]=5\lim\limits_{x\to c}g(x)=5(2)=10.$ b)$\lim\limits_{x\to c}[f(x)+g(x)]=\lim\limits_{x\to c}f(x)+\lim\limits_{x\to c}g(x)=3+2=5.$ c)$\lim\limits_{x\to c}[f(x)g(x)]=\lim\limits_{x\to c}f(x)\times\lim\limits_{x\to c}g(x)=(3)(2)=6.$ d)$\lim\limits_{x\to c}\dfrac{f(x)}{g(x)}=\dfrac{\lim\limits_{x\to c}f(x)}{\lim\limits_{x\to c}g(x)}=\dfrac{3}{2}.$
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