Determine the behavior of limits

Question

A. Limit as x approaches 1 of:

(log x)/((x-1)^2)

B. Limit as x approaches infinity of:

((x-1)^2)/(log x))

Answer 1

taking derivatives, we have

(1/x) / (2(x-1)) = 1/0 = ±∞

B is the same, since as x->∞,
(x-1)^2 / logx is the same as
1 / (logx / (x-1)^2) as x->1