## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 11 - Section 11.2 - Finding Limits Using Properties of Limits - Exercise Set - Page 1154: 63

#### Answer

The limit of a sum, $\left( f\left( x \right)+g\left( x \right) \right)$ is $\underset{x\to a}{\mathop{\lim }}\,\left( f\left( x \right)+g\left( x \right) \right)=\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)+\underset{x\to a}{\mathop{\lim }}\,g\left( x \right)$.

#### Work Step by Step

For finding the limit of a sum, first find the limit of each function in the sum. Then add each of these limits. In other words, the limit of the sum of two functions equals the sum of their limits. In limit notation, If $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=L$ and $\underset{x\to a}{\mathop{\lim }}\,g\left( x \right)=M$, then \begin{align} & \underset{x\to a}{\mathop{\lim }}\,\left( f\left( x \right)+g\left( x \right) \right)=\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)+\underset{x\to a}{\mathop{\lim }}\,g\left( x \right) \\ & =L+M \end{align} For example: Let $f\left( x \right)=x$ and $g\left( x \right)=2$. To find the limit of the sum of $f\left( x \right)$ and $g\left( x \right)$, $\underset{x\to 2}{\mathop{\lim }}\,\left( f\left( x \right)+g\left( x \right) \right)$, \begin{align} & \underset{x\to 2}{\mathop{\lim }}\,\left( f\left( x \right)+g\left( x \right) \right)=\underset{x\to 2}{\mathop{\lim }}\,f\left( x \right)+\underset{x\to 2}{\mathop{\lim }}\,g\left( x \right) \\ & =\underset{x\to 2}{\mathop{\lim }}\,x+\underset{x\to 2}{\mathop{\lim }}\,2 \\ & =2+2 \\ & =4 \end{align}

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