lim(x->1) lnx / (x-1)³,since the form of 0/0 cannot be determinated,applying L'Hospital's Rule
= lim(x->1) (1/x) / [3(x-1)²]
= (1/3)lim(x->1) 1/[x(x-1)²]
= (1/3) * 1/(1 * 0)
= ∞
Therefore the limit does not exist.