Question

Evaluate the limit if it exists.

$\underset{x\to -2}{\lim }\frac{x^2-x+6}{x+2}$

Short answer

The value of limit of the given function is$0.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{x\to -2}{\lim }\frac{x^2-x+6}{x+2}$

Step 2. Formula used.

The given function is a rational number so we can find the answer by direct substitution.

Step 3. Simplification.

Given, $\underset{x\to -2}{\lim }\frac{x^2-x+6}{x+2}$

Applying the direct substitution:

$\begin{array}{c}\underset{x\to -2}{\lim }\frac{x^2-x+6}{x+2}=\frac{(-2^2-(-2)+6)}{-2+2}\\ =\frac{4+2+6}{0}\\ =0\end{array}$

Therefore, our final answer is$0.$