Question

Please help!
Find the limit, if it exists.

Answer 1

\[\lim_{x \rightarrow -6}\frac{ 2x+12 }{ \left| x+6 \right|}\]

Answer 2

split it into 2 cases for denominator:
case 1: x > -6
\[\frac{2x+12}{x+6} = \frac{2(x+6)}{x+6} = 2\]
case 2: x < -6
\[\frac{2x+12}{-x-6} = \frac{2(x+6)}{-(x+6)} = -2\]
therefore as you approach -6 from either side you get 2 different limits, thus Limit does not exist