Chapter 14.2, Problem 18AYU

In Problems 7-42, find each limit algebraically.

$\underset{x\to 2}{\lim }\left(8x^2-4\right)$

To determine

To find: $\underset{x\to \text{ 2}}{\text{lim}}\left(8x^2-\text{ 4}\right)$

Answer to Problem 18AYU

$28$

Explanation of Solution

Given:

$\underset{x\to \text{ 2}}{\text{lim}}\left(8x^2-\text{ 4}\right)$

Formula used:

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

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

Calculation:

So $\underset{x\to \text{ 2}}{\text{lim}}\left(8x^2-\text{ 4}\right)=\underset{x\to \text{ 2}}{\lim }8x^2-\underset{x\to \text{ 2}}{\lim }4$.

$=\underset{x\to \text{ 2}}{\lim }\text{8 }\cdot \underset{x\to \text{ 2}}{\lim }{x}^2-\underset{x\to \text{ 2}}{\lim }\text{4}$

$=\text{ 8 }\times \text{ 4 }-\text{ 4}$

$=\text{ 32 }-\text{ 4}$

$=\text{ 28}$

So $\underset{x\to \text{ 2}}{\text{lim}}\left(8x^2-\text{ 4}\right)=\text{ 28}$.