practice_midterm2 - Practice Midterm 2 Math 444 Fall 2014...

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Practice Midterm 2 Math 444, Fall 2014 Sections F13–F14 Last (Family) Name : First (Given) Name : NetID : Instructions All cell phones, calculators, and other devices must be turned off and out of reach. Also, all books, notebooks, and scratch papers must be out of reach. If you run out of room on a problem page, please write ON THE BACK OF THE PAGE . The last two pages of the test are scratch papers, use them if needed, but they won’t be graded. Problem Score 1 / 20 2 / 20 3 / 20 4 / 20 5 / 20 Total / 100
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Problem 1. (20 points) Carefully read each of the following statements and circle T if the statement is TRUE and F if it is FALSE (you don’t have to justify your answer): (i) If a sequence ( x n ) converges and n N , x n ( a,b ) , then lim n x n ( a,b ) . T F (ii) The sequence sin ( 2 n ) n 2 n + cos ( n ) does not have a convergent subsequence. T F (iii) If a sequence ( x n ) is bounded and liminf n x n = limsup n x n , then ( x n ) converges. T F (iv) n ( - 1 ) n n n + 1 converges.
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