AnsHW10 - Cheung, Anthony Homework 10 Due: Nov 7 2006, 3:00...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Cheung, Anthony Homework 10 Due: Nov 7 2006, 3:00 am Inst: David Benzvi 1 This print-out should have 17 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 if the sequence { a n } converges when a n = 1 n ln 3 5 n + 1 , and if it does, find its limit. 1. limit = ln 1 2 2. limit = ln 3 5 3. limit =- ln5 4. the sequence diverges 5. limit = 0 correct Explanation: After division by n we see that 3 5 n + 1 = 3 n 5 + 1 n , so by properties of logs, a n = 1 n ln 3 n- 1 n ln 5 + 1 n . But by known limits (or use LHospital), 1 n ln 3 n , 1 n ln 5 + 1 n - as n . Consequently, the sequence { a n } converges and has limit = 0 . keywords: limit, sequence, log function, 002 (part 1 of 1) 10 points Determine whether the sequence { a n } con- verges or diverges when a n = 12 n 2 6 n + 3- 2 n 2 + 6 n + 1 , and if it does, find its limit 1. limit = 0 2. limit = 1 3 3. limit = 1 correct 4. limit = 1 2 5. the sequence diverges Explanation: After bringing the two terms to a common denominator we see that a n = 12 n 3 + 12 n 2- (6 n + 3) ( 2 n 2 + 6 ) (6 n + 3)( n + 1) = 6 n 2- 36 n- 18 6 n 2 + 9 n + 3 . Thus a n = 6- 36 n- 18 n 2 6 + 9 n + 3 n 2 . But 36 n , 18 n 2 , 9 n , 3 n 2- as n . Thus { a n } converges and has limit = 1 . keywords: sequence, convergence 003 (part 1 of 1) 10 points Determine if the sequence { a n } converges when a n = n 4 n ( n- 1) 4 n , Cheung, Anthony Homework 10 Due: Nov 7 2006, 3:00 am Inst: David Benzvi 2 and if it does, find its limit 1. sequence diverges 2. limit = e 4 correct 3. limit = e 1 4 4. limit = e- 1 4 5. limit = e- 4 6. limit = 1 Explanation: By the Laws of Exponents, a n = n- 1 n - 4 n = 1- 1 n - 4 n = h 1- 1 n n i- 4 . But 1 + x n n- e x as n . Consequently, { a n } converges and has limit = ( e- 1 )- 4 = e 4 . keywords: sequence, e, exponentials, limit 004 (part 1 of 1) 10 points Determine whether the sequence { a n } con- verges or diverges when a n = (- 1) n- 1 n n 2 + 9 , and if it converges, find the limit. 1. sequence diverges 2. converges with limit = 9 3. converges with limit =- 1 9 4. converges with limit = 0 correct 5. converges with limit = 1 9 6. converges with limit =- 9 Explanation: After division, a n = (- 1) n- 1 n n 2 + 9 = (- 1) n- 1 n + 1 n ....
View Full Document

Page1 / 8

AnsHW10 - Cheung, Anthony Homework 10 Due: Nov 7 2006, 3:00...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online