## Precalculus (6th Edition) Blitzer

The value of $\underset{x\to 1}{\mathop{\lim }}\,\left[ f\left( x \right)+g\left( x \right) \right]$ is $-2$.
To find the value of $\underset{x\to 1}{\mathop{\lim }}\,\left[ f\left( x \right)+g\left( x \right) \right]$, find the value of $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$ and the value of $\underset{x\to 1}{\mathop{\lim }}\,g\left( x \right)$. It is seen from the graph that as the value of x nears $1$ from the left or right, the value of the function $f\left( x \right)$ nears $-1$. Thus, $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)=-1$. It is seen from the graph that as the value of x nears $1$ from the left or right, the value of the function $g\left( x \right)$ nears $-1$. Thus, $\underset{x\to 1}{\mathop{\lim }}\,g\left( x \right)=-1$. Now find the value of $\underset{x\to 1}{\mathop{\lim }}\,\left[ f\left( x \right)+g\left( x \right) \right]$, \begin{align} & \underset{x\to 1}{\mathop{\lim }}\,\left[ f\left( x \right)+g\left( x \right) \right]=\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)+\underset{x\to 1}{\mathop{\lim }}\,g\left( x \right) \\ & =-1+\left( -1 \right) \\ & =-2 \end{align} Thus, the value of $\underset{x\to 1}{\mathop{\lim }}\,\left[ f\left( x \right)+g\left( x \right) \right]$ is $-2$.