Set 10

  1. (Rudin Ch. 6) #8
  2. (Rudin Ch. 6) #16.
  3. Problems X114
  4. Problems X115
  5. Problems X122
  6. Prove that: Let k and p denote a natural numbers.

(a) the limit as x approaches infinity of log(x)/x equals 0;

(b) obtain lower bounds on e^{kx}/x^p and show that e^{kx}/x^p converges to infinity as x approaches infinity.