If _ x 3 ( x^2 - ax - 3b x - 3 ) = 5 , then a + b =

Step-by-step solution

For the limit to exist and be finite, the expression must take the 0 0 form at x = 3 . Substituting x = 3 in the numerator gives: 3^2 - a(3) - 3b = 0 9 - 3a - 3b = 0 3(a + b) = 9 a + b = 3 Applying L'Hopital's rule to find the individual values: _ x 3 2x - a 1 = 5 6 - a = 5 a = 1 Substituting a = 1 into a + b = 3 gives b = 2 . Thus, a + b = 1 + 2 = 3 . Answer: 3