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Again this scrapwork is not part of the formal proof, but it is typically necessary for finding what N should be. You might be able to do the next problem without doing any scrapwork first, but don't hesitate to do scrapwork if you need it. Problem 7.1.4. Use the definition of convergence to zero to prove the following. 1 (а) lim = 0 n→∞ n2 (b) lim 1 = 0 n As the sequences get more complicated, doing scrapwork ahead of time will becomc mo ary

Again this scrapwork is not part of the formal proof, but it is typically necessary for finding what N should be. You might be able to do the next problem without doing any scrapwork first, but don't hesitate to do scrapwork if you need it. Problem 7.1.4. Use the definition of convergence to zero to prove the following. 1 (а) lim = 0 n→∞ n2 (b) lim 1 = 0 n As the sequences get more complicated, doing scrapwork ahead of time will becomc mo ary

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 7.1.4

11:06 O needed to use the inequality sin n| < 1. Again this scrapwork is not part of the formal proof, but it is typically necessary for finding what N should be. You might be able to do the next problem without doing any scrapwork first, but don't hesitate to do scrapwork if you need it. Problem 7.1.4. Use the definition of convergence to zero to prove the following. (a) lim n→∞ n2 1 (b) lim As the sequences get more complicated, doing scrapwork ahead of time will become more necessary. Example 7.1.5. Use the definition of convergence to zero to prove п+4 lim n→0 n2 +1 0. SCRAPWORK Given an ɛ > 0, we need to see how large II
Transcribed Image Text:11:06 O needed to use the inequality sin n| < 1. Again this scrapwork is not part of the formal proof, but it is typically necessary for finding what N should be. You might be able to do the next problem without doing any scrapwork first, but don't hesitate to do scrapwork if you need it. Problem 7.1.4. Use the definition of convergence to zero to prove the following. (a) lim n→∞ n2 1 (b) lim As the sequences get more complicated, doing scrapwork ahead of time will become more necessary. Example 7.1.5. Use the definition of convergence to zero to prove п+4 lim n→0 n2 +1 0. SCRAPWORK Given an ɛ > 0, we need to see how large II
11:06 make n > . This leads to the following definition. Definition 7.1.1. Let (sn) = (81, 82, s3, ...) be a sequence of real numbers. We say that (sn) converges to 0 and write lim,-> 8n = 0 provided for any e > 0, there is a real number N such that if n > N, then sn| < e. Notes on Definition 7.1.1: Definition 7.1.1. Let (sn) = (81, 82, s3,...) be a sequence of real numbers. We say that (sn) converges to 0 and write limn→0∞ $n provided for any ɛ > 0, there is a real number N such that if n > N, then Sn| < e. in-context 1. This definition is the formal version of the idea we just talked about; that is, given an arbitrary distance ɛ, we must be able to find a specific number N such that s, is within e of 0, whenever n > N. The N is the answer to the question of how large is "large enough" to put s, this close to 0. II V II
Transcribed Image Text:11:06 make n > . This leads to the following definition. Definition 7.1.1. Let (sn) = (81, 82, s3, ...) be a sequence of real numbers. We say that (sn) converges to 0 and write lim,-> 8n = 0 provided for any e > 0, there is a real number N such that if n > N, then sn| < e. Notes on Definition 7.1.1: Definition 7.1.1. Let (sn) = (81, 82, s3,...) be a sequence of real numbers. We say that (sn) converges to 0 and write limn→0∞ $n provided for any ɛ > 0, there is a real number N such that if n > N, then Sn| < e. in-context 1. This definition is the formal version of the idea we just talked about; that is, given an arbitrary distance ɛ, we must be able to find a specific number N such that s, is within e of 0, whenever n > N. The N is the answer to the question of how large is "large enough" to put s, this close to 0. II V II
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