Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2 - Page 70: 33


The statement is true

Work Step by Step

$$ \begin{array}{l}{\text { If } \lim _{x \rightarrow a} f(x) \text { and } \lim _{x \rightarrow a} g(x) \text { exist, then }} \end{array} $$ $$ \lim _{x \rightarrow a} f(x)=L_{1} , \lim _{x \rightarrow a} f(x)=L_{2} $$ where $L_{1} , L_{2}$ are constant by Theorem 1.2.2(a) we have $$ \lim _{x \rightarrow a}[f(x)+g(x)]=\lim _{x \rightarrow a} f(x)+\lim _{x \rightarrow a} g(x)=L_{1}+L_{2} $$ Thus $$ \lim _{x \rightarrow a}[f(x)+g(x)]=L_{1}+L_{2}=L_{3} $$ then $$ \lim _{x \rightarrow a}[f(x)+g(x)] $$ Therefore the statement is true
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