11. For each positive integer n, use induction to prove lim xx (In(x)) = 0. X...

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11. For each positive integer n, use induction to prove lim xx (In(x))" = 0. X 12. Let a and b be non-negative real numbers. Provide an example of an improper integral of the form f f(x)dx which converges. As well, evaluate your improper integral. 13. Let n be an integer and let a, b, x be real numbers. Evaluate possible, explain why. a .b | cos(2n) dx if possible. If not 11. For each positive integer n, use induction to prove lim xx (In(x))" = 0. X 12. Let a and b be non-negative real numbers. Provide an example of an improper integral of the form f f(x)dx which converges. As well, evaluate your improper integral. 13. Let n be an integer and let a, b, x be real numbers. Evaluate possible, explain why. a .b | cos(2n) dx if possible. If not