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Review023rdtestans

Review023rdtestans - Cheung Anthony Review 2 Due 6:00 pm...

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Unformatted text preview: Cheung, Anthony Review 2 Due: Nov 28 2006, 6:00 pm Inst: David Benzvi 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Determine whether the sequence { a n } con- verges or diverges when a n = (- 1) n 5 n + 7 7 n + 3 , and if it does, find its limit. 1. limit = 5 7 2. limit = 7 3 3. limit = 0 4. limit = 5 7 5. sequence diverges correct Explanation: After division, 5 n + 7 7 n + 3 = 5 + 7 n 7 + 3 n . Now 7 n , 3 n 0 as n , so lim n 5 n + 7 7 n + 3 = 5 7 6 = 0 . Thus as n , the values of a n oscillate be- tween values ever closer to 5 7 . Consequently, the sequence diverges . keywords: 002 (part 1 of 1) 10 points Determine if the sequence { a n } converges, when a n = 9 cos 3 n + 1 9 n + 5 , and if it does, find its limit. 1. limit = 9 2 3 2. limit = cos 1 5 3. sequence does not converge 4. limit = 9 2 correct 5. limit = 3 6. limit = 9 cos 1 5 Explanation: After division, 3 n + 1 9 n + 5 = 3 + 1 n 9 + 5 n . But 1 n , 5 n 0 as n , so lim n 3 n + 1 9 n + 5 = 3 . Consequently, since cos x is continuous as a function of x , the sequence { a n } converges and has limit = 9 cos 3 = 9 2 . keywords: sequence, convergence, limit, con- tinuity 003 (part 1 of 1) 10 points Cheung, Anthony Review 2 Due: Nov 28 2006, 6:00 pm Inst: David Benzvi 2 Determine whether the series X n = 0 3 1 2 n is convergent or divergent, and if convergent, find its sum. 1. convergent, sum =- 7 2. convergent, sum = 7 3. convergent, sum = 2 4. divergent 5. convergent, sum = 6 correct Explanation: The given series is an infinite geometric series X n = 0 ar n with a = 3 and r = 1 2 . But the sum of such a series is (i) convergent with sum a 1- r when | r | &amp;lt; 1, (ii) divergent when | r | 1. Consequently, the given series is convergent, sum = 6 . keywords: 004 (part 1 of 1) 10 points Determine whether the series X n = 1 3 n 5 n + 4 is convergent or divergent, and if convergent, find its sum....
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Review023rdtestans - Cheung Anthony Review 2 Due 6:00 pm...

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