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2. Let M> 0 be a positive integer and an > 0. CM for c>0, then (a) Prove rigorously that if lim n = n→∞ (b) Prove rigorously that lim n = C. n→∞ nM + COSM lim non cos n lim n→∞ n = 1. (c) Using the estimates from (a) and (b), prove rigorously that nM + COSM n nM- cosM n M = 1.

2. Let M> 0 be a positive integer and an > 0. CM for c>0, then (a) Prove rigorously that if lim n = n→∞ (b) Prove rigorously that lim n = C. n→∞ nM + COSM lim non cos n lim n→∞ n = 1. (c) Using the estimates from (a) and (b), prove rigorously that nM + COSM n nM- cosM n M = 1.

Advanced Engineering Mathematics
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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2. Let M > 0 be a positive integer and an > 0. (a) Prove rigorously that if lim în = c¹ for c> 0, then n→∞ (b) Prove rigorously that lim n = c. C. n→∞ nM lim n+xx0 nM lim n→∞ M n + COSM COSM n n nM - (c) Using the estimates from (a) and (b), prove rigorously that = + cost n COSM n 1. M ² = 1.
Transcribed Image Text:2. Let M > 0 be a positive integer and an > 0. (a) Prove rigorously that if lim în = c¹ for c> 0, then n→∞ (b) Prove rigorously that lim n = c. C. n→∞ nM lim n+xx0 nM lim n→∞ M n + COSM COSM n n nM - (c) Using the estimates from (a) and (b), prove rigorously that = + cost n COSM n 1. M ² = 1.
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