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討論串[微積] 數列極限問題2則
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1. Suppose that an →L. Show that if an 小於等於 M for all n,. then L 小於等於 M .. 2. Let f be a function continuous everywhere and let r be a real number.. D
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For any ε > 0, we have L–ε < a ≦ M for some n, so L ≦ M.. n. (If a–ε < b for any ε > 0, then a ≦ b.). Note that a = f(a ).. n+1 n. L = lim a = lim f(a
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Assume the contray, that is, L > M. Since a_n -> L as n -> ∞, given. ε = (L-M)/2 > 0, there is an integer N such that |a_n - L| < (L-M)/2.. Then a_n >
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