Answer
Does not exist
Work Step by Step
Check the left hand limit:
$\lim\limits_{x \to 5^-}$ $\frac{x² - 5x + 6}{x - 5}$
= $\frac{\approx25 - 25 + 6}{a very small negative number}$
= $\frac{a positive number very close to 6}{a very small negative number}$ = - ∞
Check the right hand limit:
$\lim\limits_{x \to 5^+}$ $\frac{x² - 5x + 6}{x - 5}$
= $\frac{\approx25 - 25 + 6}{a very small positive number}$
= $\frac{a positive number very close to 6}{a very small positive number}$ = ∞
$\lim\limits_{x \to 5^-}$ $\ne$ $\lim\limits_{x \to 5^+}$
Since the left and right hand limits are not equal, the limit as x approaches 5 does not exist.
A graph of the function confirms the left and right hand limits are not equal.
