Question

Would the limit of lim x-->3 (x^3 -27)/(x^2 -9) be:

9/2?

Answer 1

The numerator and denominator of the fraction can be factored and common (x-3) factors canceled to give

(x^2 + 3x +9)/(x+3)
When x = 3, that fraction is 27/6 = 9/2

You can also use L'Hopital's rule to get the same answer.

Your answer is correct.