midterm1sol

# midterm1sol - CALCULUS 153 MIDTERM 1 SOLUTIONS Please...

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Unformatted text preview: CALCULUS 153: MIDTERM 1 SOLUTIONS Please answer all questions in a blue book that’s provided to you (even the true/false). Don’t forget to write your name. There are two sides to this exam. Problem 1 (16 points) . Determine the least upper bound and greatest lower bound of the following sets, or state that they do not exist. You do not need to justify your answer (4 points each). (1) ( π, ∞ ) , (2) { x : | x- 2 | < 1 } , (3) n sin( π 2 n ) : n = 1 , 2 ,... o , (4) { . 9 ,. 99 ,. 999 ,... } . Solution (1) The lub does not exist and the glb is π . (2) The lub is 3 and the glb is 1. (3) The lub is 1 and the glb is 0. (4) The lub is 1 and the glb is .9. Problem 2 (21 points) . For each of the following sequences, determine whether the sequence converges or diverges. If it converges, find its limit. Show your work. (7 points each). (1) a n = (2 n ) 1 /n ; (2) b n = cos π + ln n n . (3) c n = 3 n n !...
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## This note was uploaded on 04/07/2008 for the course MATH 153 taught by Professor Masson during the Fall '07 term at UChicago.

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midterm1sol - CALCULUS 153 MIDTERM 1 SOLUTIONS Please...

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