MATH 0413 Final: math0413-Final Exam Review
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Math 0413 - review: let an = {2nk : k n} for each n n. prove that. An = : let the set t (8) = {all subsets containing 8 elements of n}. 2 (cid:17)2: prove that, if x q and y is irrational, then x + y is irrational. Is x2 + y2 irrational: solve the following inequalities for x r: 4 |x 1| + |x + 2| 5: show that. 1 n(cid:21) = {0}: use the de nition of the limit of a sequence to establish the following limit: lim n n2 + 1. 2: suppose that xn 0 for all n n and lim, if n lim n xn = a > 0, show that there exists k n, such that, xn > a. Show that lim n xn = 0: suppose that xn is bounded and lim n yn = 0.
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