Prove that lim x0+ ln(x) = . Given N < 0 we need > 0 so that ln(x) ---Select--- whenever 0 < x < ? ; that is, x = e^ln(x) ? e^N whenever 0 < x < ?. This suggests that we take = eN. If 0 < x < eN, then ln(x) ? ln(eN) = N. By the definition of a limit, lim x0+ ln(x) = .