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Problem 7.1.14. (a) Provide a rigorous definition for lim sn # s. (b) Use your definition to show that for any real number a, lim ((-1)")+ a. Hint. Choose ɛ = 1 and use the fact that a - (-1)" < 1 is equivalent to (-1)" – 1 < a < (-1)" +1 to show that no choice of N will work for this ɛ.

Problem 7.1.14. (a) Provide a rigorous definition for lim sn # s. (b) Use your definition to show that for any real number a, lim ((-1)")+ a. Hint. Choose ɛ = 1 and use the fact that a - (-1)" < 1 is equivalent to (-1)" – 1 < a < (-1)" +1 to show that no choice of N will work for this ɛ.

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
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Please help me solve problem 7.1.14

11:09 O our intuition was, in fact, correct and do so in a very prescribed manner. For example, if b > 0 is a fixed number, then you would probably say as n approaches infinity, b() approaches 6º = 1. After all, we did already prove that lim,,→, = 0. We should be able to back up this intuition with our rigorous definition. Problem 7.1.13. Let b > 0. Use the definition to prove lim b) 1. Hint. You will probably need to separate this into two cases: 0 < b < 1 and b > 1. Problem 7.1.14. (a) Provide a rigorous definition for lim sn + s. (b) Use your definition to show that for any real number a, lim ((-1)")+ a. Hint. Choose e = 1 and use the fact that a – (-1)"| < 1 is equivalent to (-1)" – 1 < a < (-1)" +1 to show that no choice of N will work for this ɛ. II II
Transcribed Image Text:11:09 O our intuition was, in fact, correct and do so in a very prescribed manner. For example, if b > 0 is a fixed number, then you would probably say as n approaches infinity, b() approaches 6º = 1. After all, we did already prove that lim,,→, = 0. We should be able to back up this intuition with our rigorous definition. Problem 7.1.13. Let b > 0. Use the definition to prove lim b) 1. Hint. You will probably need to separate this into two cases: 0 < b < 1 and b > 1. Problem 7.1.14. (a) Provide a rigorous definition for lim sn + s. (b) Use your definition to show that for any real number a, lim ((-1)")+ a. Hint. Choose e = 1 and use the fact that a – (-1)"| < 1 is equivalent to (-1)" – 1 < a < (-1)" +1 to show that no choice of N will work for this ɛ. II II
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