Math 132 Exam 2 Spring 2016 Name ID Number Section Number Section Instructor Day Time MWF 10 10 MWF 9 05 Nikolaou MWF 11 15 Nikolaou MWF 12 20 Zhao Zhao Wen Wen Yaping Lowell MW 2 30 MW 4 00 TuThu 8 30 TuThu 10 00 1 2 3 4 5 6 7 8 Section Instructor Day Time 9 10 11 12 13 15 16 Sunukjian TuThu 11 30 Benincasa TuThu 4 00 MWF 11 15 MWF 12 20 MWF 1 25 TuThu 11 30 TuThu 1 00 Farelli Bates Hart Le Johnson No papers or notes may be used You may use a calculator on this exam Please don t just give an answer Clearly explain how you get it pro viding appropriate mathematical details An answer of convergent or divergent with no supporting work will be awarded zero points This is a 2 hour exam Question MC Total Out of 25 6 Out of 20 7 Out of 15 8 Out of 20 9 Out of 20 Total Out of 100 a a a a Grade cid 107 b cid 107 b cid 107 b cid 107 b 1 Mutiple Choice Section Choose the one option that best answers the question There is no partial credit for questions 1 5 1 5 points For what values of r does the following integral converge cid 90 r 1 x2 dx 2 5 points Which one of the following series represents the repeating dec A For all values of r B r 0 C r 0 D Never imal 0 454545 A 45 cid 19 n 1 cid 19 n 1 cid 88 n 1 cid 88 n 1 cid 88 n 1 cid 88 n 1 cid 18 1 10 cid 18 1 100 cid 18 1 100 cid 18 1 100 45 100 45 100 cid 19 n 1 cid 19 n B D C 45 3 5 points Which of the following statements is false A If the series an converges then lim n an 0 cid 88 n 1 B If lim n an 0 then the series an converges C If lim n D If lim n an cid 54 0 then the series an diverges an 1 then the sequence an n 1 converges cid 88 n 1 cid 88 n 1 2 4 5 points Given the following series which of the following converge 2n n3 cid 88 I n 1 cid 88 II 5 n III n 1 cid 88 n 1 n 8 14n 9 A I II and III B I and II C I only D II and III A B C 3 5 1 2 5 6 D 1 5 5 points What is the sum of the series cid 88 n 0 3n 1 5n Please ll in your letter answer for questions 1 5 below 1 2 3 4 5 3 Free Response Portion Show all work for each of the following ques tions Partial credit may be awarded for questions 6 10 You will receive no credit for an answer of convergent or divergent without supporting work 6 a 10 points Evaluate the following integral cid 90 x 1 2x2 x 3 dx 4 6 b 10 points Does the following integral converge or diverge If it converges what does it converge to cid 90 3 2 3 x 2 2 dx 5 7 a 5 points Does the series converge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 2 sin2 n n2 1 6 7 b 10 points Does the series converge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 2 n 1 n 2n 1 ln n n 7 8 a 10 points Does the series converge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 1 6n2e n3 8 8 b 10 points Does the series converge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 2 n2 2n 3 n3 n 1 9 9 a 10 points Does the series absolutely converge conditionally con verge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 1 1 n 35n 3n 2n 10 9 b 10 points Does the series absolutely converge conditionally con verge or diverge State which test you used and clearly show that the series meets the conditions to use this test cid 88 n 1 1 n n 1 n2 7 11 This page is intentionally left blank for additional work 12