Question

In Problems 33– 44, find the one-sided limit.

$\underset{x\to 2^{+}}{\lim \frac{x^2-4}{x-2}}$

Short answer

The limit values

$\underset{x\to 2^{+}}{\lim \frac{x^2-4}{x-2}}=4$

Step-by-step solution

step 1.introduction

Given limit

$\underset{x\to 2^{+}}{\lim \frac{x^2-4}{x-2}}$

step 2.explanation

consider the limit

$$\begin{gathered} \underset{x\to 2^{+}}{\lim \frac{x^2-4}{x-2}} \\ \underset{x\to 2^{+}}{\lim \frac{(x+2)(x-2)}{(x-2)}=(2+2)} \\ =4 \end{gathered}$$

step 3. the solution

the limit value

$\underset{x\to 2^{+}}{\lim \frac{x^2-4}{x-2}}=4$