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PracticeTest3 - 6 16 5 13 4 10 3 7 2 4 6 Use a geometric...

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Practice Test #3 MAC2312 Directions: Use this practice test as a guide for your study for Test #3. This exam is not comprehensive, so study your quiz, class notes and homework problems in addition to completing this exam. Solutions are posted on the course websit e under “Solutions”. 1) Find the limit, if it exists: a) 2 2 1 1 ) ln( lim x x x b) 2 3 1 lim x x x 2) Consider the improper integral 7 5 2 3 dx xe x . a) Why is this integral improper? b) Evaluate the integral. c) Does the integral converge or diverge? _____ Why? 3) If you were to evaluate the integral 8 2 2 5 4 dx x x x , how would you set it up with limits? Set up but do not evaluate the integral. 4) Find the limit (if it exists) as n approaches positive infinity of a sequence whose nth term is 1 3 2 n n a n . 5) Find an nth term of a sequence whose first five terms are ,...
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Unformatted text preview: ,... 6 16 , 5 13 , 4 10 , 3 7 , 2 4 6) Use a geometric series to write ____ 345 . as a ratio of two integers. 7) Use the nth-Term Test to determine if 1 7 ! 5 ! 3 n n n diverges. 8) Apply the Integral Test to determine if the series 1 2 1 4 2 n n n will converge or diverge. Show work for testing the conditions of the Integral Test, and then apply the test. 9) Determine what type of series each is by converting to the proper form , then determine if it converges or diverges and explain why. a) 3 7 1 4 n n b) 1 4 3 1 n n n Type of series: _________ Type of series: _________ Converge or diverge? _______ Converge or diverge? _______ Why? Why? 10) Use the Limit Comparison Test to determine if the series 1 3 3 2 4 n n n converges or diverges....
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