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5 = 0 n-x n² (a) lim 7n n-∞ n² +3 (c) lim = 0 (b) lim - n→∞ n +4 11 (d) lim n-∞ 1-n² = 0 = 0

5 = 0 n-x n² (a) lim 7n n-∞ n² +3 (c) lim = 0 (b) lim - n→∞ n +4 11 (d) lim n-∞ 1-n² = 0 = 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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#3 (a)-(p)

Thank you so so much in advance!!!

Need to prove the limit statements using these steps. (as shown in image 2)

 

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.)
5 n→∞ n² (a) lim 7n (c) lim non² +3 (e) lim 3n non +4 (g) lim = 0 (i) lim - (k) lim n-x 7n-1 5n n-∞ 11+ n² (m) lim = 3 3n+4 3 7 (o) lim = 0 n→∞ n² + n n² - 2 n - 2n² n→∞ 3n² + 1 n² + 3n n-∞ 10-n² = 0 = 1 1 2 3 -1 3 n→∞n +4 (b) lim 11 n-∞ 1-n² (d) lim 2n - 5 n→∞ n-6 (f) lim 2n n-∞ 1-5n (h) lim (j) lim = 0 n n→∞ 1+8n² (1) lim (n) lim = = 0 (p) lim = 2 || 8n² +3 n-x 5n² - 2n = 2 5 0 = 2n²-1 n→∞ n² - 5n - 7 n² + 6n n→∞ n³ - 5n+1 815 8 = 2 = 0 = 3. Use the methods of this section to prove each of the limit statements (a)-(p) given in Exercise 2 above.
Transcribed Image Text:5 n→∞ n² (a) lim 7n (c) lim non² +3 (e) lim 3n non +4 (g) lim = 0 (i) lim - (k) lim n-x 7n-1 5n n-∞ 11+ n² (m) lim = 3 3n+4 3 7 (o) lim = 0 n→∞ n² + n n² - 2 n - 2n² n→∞ 3n² + 1 n² + 3n n-∞ 10-n² = 0 = 1 1 2 3 -1 3 n→∞n +4 (b) lim 11 n-∞ 1-n² (d) lim 2n - 5 n→∞ n-6 (f) lim 2n n-∞ 1-5n (h) lim (j) lim = 0 n n→∞ 1+8n² (1) lim (n) lim = = 0 (p) lim = 2 || 8n² +3 n-x 5n² - 2n = 2 5 0 = 2n²-1 n→∞ n² - 5n - 7 n² + 6n n→∞ n³ - 5n+1 815 8 = 2 = 0 = 3. Use the methods of this section to prove each of the limit statements (a)-(p) given in Exercise 2 above.
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