Question

In Problems 7– 42, find each limit algebraically

$\underset{x\to 2}{\lim }(3x+2)$

Short answer

The value is$8$

Step-by-step solution

Step 1. Given Information

The given limit and function is$\underset{x\to 2}{\lim }(3x+2)$

We need to find the value of the limit.

Step 2. Value of the limit

We know,

$\underset{x\to c}{\lim }\left[f\right(x)+g(x\left)\right]=\underset{x\to c}{\lim }f\left(x\right)+\underset{x\to c}{\lim }g\left(x\right)$

Therefore,

$$\begin{gathered} \underset{x\to 2}{\lim }(3x+2)=\underset{x\to 2}{\lim }3x+\underset{x\to 2}{\lim }2 \\ =\left[\underset{x\to 2}{\lim }3\right]\left[\underset{x\to 2}{\lim }x\right]+\underset{x\to 2}{\lim }2 \\ =\left[3\right]\left[2\right]+2 \\ =6+2 \\ =8 \end{gathered}$$