calc hw 2

# calc hw 2 - lawrence(cdl678 – Homework 2 – Odell...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lawrence (cdl678) – Homework 2 – Odell – (56280) 1 This print-out should have 37 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Compute the value of lim n →∞ 2 a n b n 3 a n − 2 b n when lim n →∞ a n = 6 , lim n →∞ b n = − 2 . 1. limit = 12 11 2. limit = 13 11 3. limit = − 12 11 correct 4. limit = − 13 11 5. limit doesn’t exist Explanation: By properties of limits lim n → 2 2 a n b n = 2 lim n →∞ a n lim n →∞ b n = − 24 while lim n →∞ (3 a n − 2 b n ) = 3 lim n →∞ a n − 2 lim n →∞ b n = 22 negationslash = 0 . Thus, by properties of limits again, lim n →∞ 2 a n b n 3 a n − 2 b n = − 12 11 . 002 10.0 points If lim n →∞ a n = 7 , determine the value, if any, of lim n →∞ a n − 9 . 1. limit doesn’t exist 2. limit = 16 3. limit = − 2 4. limit = 7 9 5. limit = 7 correct Explanation: To say that lim n →∞ a n = 7 means that a n gets as close as we please to 7 for all sufficiently large n . But then a n − 9 gets as close as we please to 7 for all sufficiently large n . Consequently, lim n →∞ a n − 9 = 7 . 003 10.0 points Determine if the sequence { a n } converges when a n = 1 n ln parenleftbigg 6 5 n + 4 parenrightbigg , and if it does, find its limit. 1. limit = ln 6 5 2. limit = 0 correct 3. limit = − ln5 4. limit = ln 2 3 5. the sequence diverges Explanation: lawrence (cdl678) – Homework 2 – Odell – (56280) 2 After division by n we see that 6 5 n + 4 = 6 n 5 + 4 n , so by properties of logs, a n = 1 n ln 6 n − 1 n ln parenleftbigg 5 + 4 n parenrightbigg . But by known limits (or use L’Hospital), 1 n ln 6 n , 1 n ln parenleftbigg 5 + 4 n parenrightbigg −→ as n → ∞ . Consequently, the sequence { a n } converges and has limit = 0 . 004 10.0 points Determine if the sequence { a n } n converges when a n = 7 n 3 n − 1 and if it does, find its limit when 1. converges with limit = 3 7 2. converges with limit = 7 2 3. converges with limit = 0 4. converges with limit = 7 3 correct 5. the sequence diverges Explanation: After division by n we see that a n = 7 3 − 1 n −→ 7 3 as n → ∞ . Thus { a n } n converges and has limit = 7 3 . 005 10.0 points Determine if the sequence { a n } converges, and if it does, find its limit when a n = 7 n + ( − 1) n 4 n + 3 . 1. converges with limit = 2 2. converges with limit = 1 3. sequence does not converge 4. converges with limit = 7 4 correct 5. converges with limit = 3 2 Explanation: After division by n we see that a n = 7 + ( − 1) n n 4 + 3 n . But ( − 1) n n , 3 n −→ as n → ∞ , so a n → 7 4 as n → ∞ . Conse- quently, the sequence converges and has limit = 7 4 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 19

calc hw 2 - lawrence(cdl678 – Homework 2 – Odell...

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

View Full Document
Ask a homework question - tutors are online