Question

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

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

Short answer

The value is$\frac{3}{2}$

Step-by-step solution

Given information

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

Sketching the graph

The graph is

Checking the limit

For $x\to -2+$, $x$is close to $-2$but greater than $-2$so

$\underset{x\to -2^{+}}{\lim }\left(\frac{x^2+x-2}{x^2+2x}\right)=\frac{3}{2}$