Help, evaluate the limit?

alex

x<0 ---> |x| = -x hence lim = 0

Johnathan

Agree with Alex. If x approaches negative infinity, then the numerator is essentially x - x, which is 0. It matters not about the denominator other than x = -1 (0/0 -- indeterminate here), as it becomes a bigger negative number; you have 0 divided by a minus, which is 0. This limit is 0.