Question

Lim of (x^3-13x+12)/(x^3-14x+15) as x approaches 3 without using L hopital's rule.

Answer 1

Lim of (x^3 - 13x + 12)/(x^3 - 14x + 15) as x approaches 3 =
Lim of (x - 3)(x^2 + 3x - 4)/(x - 3)(x^2 + 3x - 5) as x approaches 3 = Lim of (x^2 + 3x - 4)/(x^2 + 3x - 5) as x approaches 3 = ((3)^2 + 3(3) - 4)/((3)^2 + 3(3) - 5) = (9 + 9 - 4)/(9 + 9 - 5) = 14/13