Chapter 14.2, Problem 15AYU

In Problems 7-42, find each limit algebraically.

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

To determine

To find: $\underset{x\to 2}{\text{lim}}\left(3x+2\right)$

Answer to Problem 15AYU

Solution:

$8$

Explanation of Solution

Given:

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

Formula used:

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

And,

$\underset{x\to \text{ c}}{\text{lim}}b=b\text{ and }\underset{x\to \text{ c}}{\text{lim}}x=c$

Calculation:

So $\underset{x\to 2}{\text{lim}}\left(3x+2\right)=\underset{x\to 2}{\text{lim}}3x+\underset{x\to 2}{\text{lim}}2$.

$=\underset{x\to 2}{\text{lim}}3\cdot \underset{x\to 2}{\text{lim}}x+\underset{x\to 2}{\text{lim}}2$

$=3\times 2+2$

$=6+2$

$=8$

So $\underset{x\to 2}{\text{lim}}\left(3x+2\right)=8$.