Lim as x approaches 2 of (x^2-kx+4)/(x^3-8)
if k = -2, there's no problem. The fraction is just 1/(x-2), so the limit is ∞
Otherwise, the numerator is only ever zero if k>4, at
x = 1/2 (k±√(k^2-16))
In any case, as x->2, the numerator is not zero, the the limit is ±∞