Math 132 Exam 2 Fall 2018 Name Signature Student ID Number Section Number Section Instructor Day Time Section Instructor Day Time MWF 9 05 1 6 MWF 10 10 7 2 MWF 11 15 8 3 4 MWF 12 20 9 5 Correia Correia Duan Nguyen Hacking MWF 1 25 TuThu 1 00 Farelli Farelli TuThu 2 30 Destromp MWF 10 10 MWF 1 25 Torres Dul MWF 8 00 Nakamura TuThu 8 30 10 11 Calculators papers phones smart watches any device or notes are not permitted on this exam The use of any of these items is considered Academic Dishonesty In the free response section do not just give an answer Clearly explain how you get it providing appropriate mathematical details An answer with no corresponding work will be awarded zero points This is a 2 hour exam Question Multiple Choice Questions Out of 25 6 Out of 10 Grade 7 Out of 10 8 Out of 10 9 Out of 10 10 Out of 10 11 Out of 10 12 Out of 15 Total Out of 100 Multiple Choice Section Choose the one option that answers the question There is no partial credit for questions 1 5 Only answers written in the answer blank will be graded 1 5 points Which of the following is true about the series below 1 2 2 4 A B C The series converges to 0 by the Test for Divergence The series diverges by the Test for Divergence The Test for Divergence is inconclusive for this series Answer 1 D The series converges to 1 by the Test for Divergence 2 2 5 points Which of the following is true about the series below B The series converges to Answer 2 A The series converges to C The series converges to D The series diverges 1 8 9 8 1 9 9 1 2 4 3 5 points Suppose 0 and 0 for all If lim 1 which of the following is true A No conclusions about the convergence of can be made with the given information B converges if converges No conclusion about divergence of can be made C diverges if diverges No conclusion about convergence of can be made D converges if converges and diverges if diverges Answer 3 5 points Consider the sequence below ln 3 2 1 ln 2 9 Which of the following is true A The sequence converges to 0 The sequence converges to ln 3 B C D The sequence diverges The sequence converges to ln 2 Answer 4 3 5 5 points If which of the following is true 2 1 3 4 I 1 II 1 III 1 IV 1 is convergent is convergent is divergent is divergent A B C D I and II are true III and IV are true I and IV are true II and III are true Answer 5 4 Free Response Section Show all work for each of the following questions Partial credit may be awarded for questions 6 12 6 10 points Determine if the integral converges or diverges If it converges find the value 6 ln 0 5 7 10 points Determine if the series converges or diverges Clearly state which test you used and show that this series meets the requirements to use this test 2 4 1 5 6 8 10 points Determine if the series converges or diverges Clearly state which test you used and show that this series meets the requirements to use this test 1 3 4 2 7 9 10 points Determine if the series converges or diverges Clearly state which test you used and show that this series meets the requirements to use this test 1 2 4 3 5 1 8 10 10 points Use the INTEGRAL TEST to determine if the series is convergent or divergent Clearly show that this series meets the requirements to use this test 1 4 2 3 2 9 11 10 points Determine if the series converges or diverges Clearly state which test you used and show that this series meets the requirements to use this test 1 5 1 2 1 10 12 15 points Determine if the series is absolutely convergent conditionally convergent or divergent Clearly state which test s you used and show that this series meets the requirements to use this test 1 1 7 3 11