Question

How do you evaluate the limit of `(3x+9)/(x^2-5x-24)` as `x->2`?

Answer 1

By substitution.

Explanation:

If `x` is approaching `2`, then

the numerator is approaching `3(2)+9 = 6+9 = 15`

and the denominator is approaching `(2)^2-5(2)-24 = 4-10-24 = -30`

So the limit of the quotient is `15/(-30) = -1/2`