created-9-24-04 - Limits Limit # 1. lim n sin n 1 1 = lim x...

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Limits Limit # 1. lim n →∞ n sin 1 n = lim x →∞ x sin 1 x = lim x →∞ sin 1 x 1 x = lim θ 0 sin θ θ = 1 by Red #2, p 190. Definition 1. A sequence is a function whose domain is the set of all positive integers. Definition 2. Let { a n } be a sequence of real numbers and let L be a real number. Then (a) lim n →∞ a n = L iF the following condition holds: ±or each open interval U centered at L, a n is in U from some index N onward. (b) lim n →∞ a n = iF the following holds: ±or each interval U = ( M, ], a n is in U from some index onward.
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This note was uploaded on 05/17/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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