Sequences 1) Could there be a sequence {an}= {f(n)} such that limitz0 f (x) exists, but limit n00An does not? 2) Could limit n oan exists but not for limit, f (x)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Sequences**

1) Could there be a sequence \( \{a_n\} = \{f(n)\} \) such that \( \lim_{x \to \infty} f(x) \) exists, but \( \lim_{n \to \infty} a_n \) does not?

2) Could \( \lim_{n \to \infty} a_n \) exist but not for \( \lim_{x \to \infty} f(x) \)?

3) Discuss your options with other students; you can give an example to enhance your reasoning.
Transcribed Image Text:**Sequences** 1) Could there be a sequence \( \{a_n\} = \{f(n)\} \) such that \( \lim_{x \to \infty} f(x) \) exists, but \( \lim_{n \to \infty} a_n \) does not? 2) Could \( \lim_{n \to \infty} a_n \) exist but not for \( \lim_{x \to \infty} f(x) \)? 3) Discuss your options with other students; you can give an example to enhance your reasoning.
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