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These are alternative definitions of the limit of sequences. Can you please help identify what is wrong with each of the definitions?

These are alternative definitions of the limit of sequences. Can you please help identify what is wrong with each of the definitions?

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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These are alternative definitions of the limit of sequences. Can you please help identify what is wrong with each of the definitions?

 

 

6. limn- an = a if 7. lim xan = a if 8. limn- an = a if 9. limnan = a if 10. limn-vocan a if 11. limn-ro On = a if Ve> 0 3N EN such that Vn2 N (an - a)³ < E -a|< 1/ Ve > 0 3N EN such that Vn2 N³ Jan - al V E Ve> 0 3N EN such that Vn2 N lan - a < N Ve > 0 3N EN such that Vn 2 Njan - al < 100€ Ve > 0 3N EN such that Vn 2 N lan - al < Ne Ve> 0 3N EN such that Vn 2 N ||an| - la|| <s
Transcribed Image Text:6. limn- an = a if 7. lim xan = a if 8. limn- an = a if 9. limnan = a if 10. limn-vocan a if 11. limn-ro On = a if Ve> 0 3N EN such that Vn2 N (an - a)³ < E -a|< 1/ Ve > 0 3N EN such that Vn2 N³ Jan - al V E Ve> 0 3N EN such that Vn2 N lan - a < N Ve > 0 3N EN such that Vn 2 Njan - al < 100€ Ve > 0 3N EN such that Vn 2 N lan - al < Ne Ve> 0 3N EN such that Vn 2 N ||an| - la|| <s
Expert Solution
Step 1

Given: limn→∞an=a if ∀ε>0∃N∈ℕ such that ∀n≥N  an-a3<ε

To Find: Identify what is wrong with the given definitions of the limit of the sequence.

"As per the policy we are allowed to answer only the first question please repost the other question separately.

 

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