Answer
Does not exist
Work Step by Step
Simplify:
$\frac{x²+3x}{x²-x-12}$
$\frac{x(x+3)}{(x-4)(x+3)}$
$\frac{x}{x-4}$ , x $\ne$ - 3
Check the left hand limit:
$\lim\limits_{x \to 4^- }$ $\frac{x}{x-4}$
= $\frac{positivenumbercloseto4}{very small negative number}$ = - ∞
Check the right hand limit:
$\lim\limits_{x \to 4^+ }$ $\frac{x}{x-4}$
= $\frac{positivenumbercloseto4}{very small positive number}$ = ∞
$\lim\limits_{x \to 4^- }$ $\ne$ $\lim\limits_{x \to 4^+ }$
The left and right hand limits are not equal therefore the limit does not exist.
A graph of the function confirms the left and right limits don't match.
