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: 38

Answer

a) $8.$ b)$\dfrac{11}{4}.$ c)$\dfrac{3}{2}.$ d) $\dfrac{8}{3}.$

Work Step by Step

Using Theorem $1.2:$ a)$\lim\limits_{x\to c}[4f(x)]=4[\lim\limits_{x\to c}f(x)]=4(2)=8.$ b)$\lim\limits_{x\to c}[f(x)+g(x)]=\lim\limits_{x\to c}f(x)+\lim\limits_{x\to c}g(x)=2+\dfrac{3}{4}=\dfrac{11}{4}.$ c)$\lim\limits_{x\to c}[f(x)g(x)]=(\lim\limits_{x\to c}f(x))(\lim\limits_{x\to c}g(x))=2\times\dfrac{3}{4}=\dfrac{3}{2}.$ d)$\lim\limits_{x\to c}\dfrac{f(x)}{g(x)}=\dfrac{\lim\limits_{x\to c}f(x)}{\lim\limits_{x\to c}g(x)}=\dfrac{2}{\frac{3}{4}}=\dfrac{8}{3}.$
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