Question

In Problems 7– 42, find each limit algebraically

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

Short answer

The value of the limit is$\underset{x\to 2}{\lim }\left(8x^2-4\right)=28$

Step-by-step solution

Step 1. Given Information

The given limit function is$\underset{x\to 2}{\lim }\left(8x^2-4\right)$

We need to find the value of the limit.

Step 2. Expanding the limit

It is known,

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

Therefore,

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

Step 3. Value of the limit

On solving The simplified expression,

$$\begin{gathered} \underset{x\to 2}{\lim }\left(8x^2-4\right)=\underset{x\to 2}{\lim }8x^2-\underset{x\to 2}{\lim }4 \\ =\{8\times {\left(2\right)}^2\}-4 \\ =\{8\times 4\}-4 \\ =32-4 \\ =28. \end{gathered}$$