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n n→∞ 1+8n2² (j) lim = 0

n n→∞ 1+8n2² (j) lim = 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
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Prove this limit statement using method as shown in image 2.

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n n→∞ 1+8n² (i) lim = 0
Transcribed Image Text:n n→∞ 1+8n² (i) lim = 0
SUMMARY: HOW TO PROVE lim xn = L 818 1. Let & > 0. 2. Find a real number r such that xn - L < e for all n ≥ r. (This is what we did in Part (c) of Examples 2.1.5 and 2.1.7.) 3. Let no denote any natural number ≥r (found in Step 2). (The Archimedean property guarantees the existence of this no.) 4. Prove directly that for this value of no, n ≥ no ⇒ |xn - L| < E. (This is what we did in Examples 2.1.6 and 2.1.8.)
Transcribed Image Text:SUMMARY: HOW TO PROVE lim xn = L 818 1. Let & > 0. 2. Find a real number r such that xn - L < e for all n ≥ r. (This is what we did in Part (c) of Examples 2.1.5 and 2.1.7.) 3. Let no denote any natural number ≥r (found in Step 2). (The Archimedean property guarantees the existence of this no.) 4. Prove directly that for this value of no, n ≥ no ⇒ |xn - L| < E. (This is what we did in Examples 2.1.6 and 2.1.8.)
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