Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Exercise Determine whether the sequence (an) given by an n³ 3n² - 2 converges, and find its limit if it does. Name any results or rules that you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. n³ 3n²-1 (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include statements or omissions that follows logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) For n=1,2,..., we have n³ 3n² - 2 n³ 3n²-2 n³ 3n2 - 2 lanl VI (since n³ 3n² 2n + + + 3n2 n³ n³ 3n²-1 n³ 3n² - 2 n³ 3n² n.³ 3n2 - 1 > 0 and (by the Triangle Inequality) n³ 3n² - 1 > 0)

Exercise Determine whether the sequence (an) given by an n³ 3n² - 2 converges, and find its limit if it does. Name any results or rules that you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. n³ 3n²-1 (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include statements or omissions that follows logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) For n=1,2,..., we have n³ 3n² - 2 n³ 3n²-2 n³ 3n2 - 2 lanl VI (since n³ 3n² 2n + + + 3n2 n³ n³ 3n²-1 n³ 3n² - 2 n³ 3n² n.³ 3n2 - 1 > 0 and (by the Triangle Inequality) n³ 3n² - 1 > 0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
This question concerns the following exercise. Exercise Determine whether the sequence (an) given by n.³ n.³ an = 3n²2 - 2 3n² - 1 converges, and find its limit if it does. Name any results or rules that you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include statements or omissions that follows logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) For n=1,2,..., we have n.³ 3n2 - 2 n³ 3n² - 2 23 3n² - 2 |an| 73 VI = (since n.³ 3n² 2n 3 + n³ 3 3n²-1 + n³ 3n2 - 1 n³ 3n2 - 1 + n³ 3n² - 2 n³ 3n² > 0 and (by the Triangle Inequality) n.³ 3 3n² - 1 > 0) Now 2n/3→ ∞o as noo, so by the Squeeze Rule (Theorem D18) it follows that lan →∞ as n→∞0. Therefore an →∞o as noo. Thus (an) is divergent. (b) Write out a correct solution to the exercise.
Transcribed Image Text:This question concerns the following exercise. Exercise Determine whether the sequence (an) given by n.³ n.³ an = 3n²2 - 2 3n² - 1 converges, and find its limit if it does. Name any results or rules that you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. (a) Explain why the following solution to this exercise is incorrect and/or incomplete, identifying three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include statements or omissions that follows logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) For n=1,2,..., we have n.³ 3n2 - 2 n³ 3n² - 2 23 3n² - 2 |an| 73 VI = (since n.³ 3n² 2n 3 + n³ 3 3n²-1 + n³ 3n2 - 1 n³ 3n2 - 1 + n³ 3n² - 2 n³ 3n² > 0 and (by the Triangle Inequality) n.³ 3 3n² - 1 > 0) Now 2n/3→ ∞o as noo, so by the Squeeze Rule (Theorem D18) it follows that lan →∞ as n→∞0. Therefore an →∞o as noo. Thus (an) is divergent. (b) Write out a correct solution to the exercise.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS