For each of the given limits$,$ determine what would be the immediate conclusion if we try to apply Direct Substitution to it$.($Match each limit question with one of the possible conclusions.$)$

$\underset{x2}{lim}\frac{x^2-6}{x^2-7x+10}$

Indeterminate form $\frac{0}{0},$ so further

$\underset{x2}{lim}\frac{x^2-4}{x^2-7x+10}$

work is needed.

$2.$ The limit is definitely equal to $0.$

$\underset{x2}{lim}\frac{x^2-4}{x^2-7x+12}$

The limit definitely doesn't exist.