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Unformatted text preview: lim n a n = L . 1 2 CALCULUS 153: SAMPLE MIDTERM 1 Problem 5 (14 points) . Prove that if T is a subset of S , then sup T sup S . Problem 6 (20 points) . For each of the following give an example, or state that no example exists (you do not need to justify your answer). (1) A set S whose least upper bound is not an element of S . (2) A set of negative numbers whose least upper bound is strictly positive. (3) A set of rational numbers whose least upper bound is irrational. (4) A set of irrational numbers whose least upper bound is rational. (5) A sequence thats bounded but divergent....
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