Problems

In Problems 1-7, verify the inequalities.

In Problems 8-23 evaluate the limit.

24            Prove that the function y = x^x, x ≥ 1, is increasing.

25            Prove that if a > 0 and lim_x→c f(x) = L, then lim_x→c a^f(x) = a^L.

26            Prove that for each real number r, the function y = x^r, x > 0, is continuous.