Chapter 14.3, Problem 39AYU

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

To determine

To find: One sided limit: $\underset{x\to 2^{+}}{\lim }\left(\frac{x^2-4}{x-2}\right)$.

Answer to Problem 39AYU

4

Explanation of Solution

Given:

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

Calculation:

Since $\underset{x\to 2^{+}}{\lim }$; so $x\ne 2$.

Then we have,

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