Find Limit[x -> 3] f(x), where f(x) = (x^4 - 81)/(2x^2 - 5x - 3)
f(x) simplifies, by factoring, down to
(x^2 - 9)(x^2 + 9)(2x + 1)(x - 3) =
(x - 3)(x + 3)(x^2 + 9)/ (2x +1)(x - 3) =
(x + 3)(x^2 + 9)/(2x + 1)
As x -> 3, the numerator (x + 3)(x^2 + 9) -> 6*18 = 108
As x -> 3, the denominator, (2x + 1) -> 7
As x -> 3, f(x) -> 108/7 = 15.428
Answer: Limit of f(x), as x -> 3, is 15.428