Answer
$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$ doesn't exist.
Work Step by Step
$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$
Try to find the limit applying direct substitution:
$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}=\dfrac{(-2)^{2}-(-2)+6}{-2+2}=\dfrac{4+2+6}{0}=\infty$
$\lim_{x\to\ -2}\dfrac{x^{2}-x+6}{x+2}$ doesn't exist.
