(1) Suppose that (an)neN is a sequence of positive numbers that converges to a positive real number a. (a) Show that there exists an M such that an > for all n > M. (b) Prove that lim loge (an) = loge (a) using the definition of convergence. (You may use the inequality | loge (x) - loge(y)| ≤ for x, y > 0.) |x-y min{x,y}

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