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Консультация № 69897
07.01.2007, 18:04
0.00 руб.
0
2
2
Здравствуйте Эксперты! Помогите вычислить предел. И как вообще решаются пределы такого типа?
lim (x->беск) ((n-3)/(n+1))^(2n)
lim (x->беск) ((n-3)/(n+1))^(2n)
Обсуждение
Неизвестный
07.01.2007, 18:23
общий
это ответ
Здравствуйте, Art120684!
(n-3)/(n+1) = (1-3/n) / (1+1/n).
Сводим к пределу вида (1+1/x)^x (этот предел равен е) числитель и знаменатель.
(1-3/n)^2n = ((1-3/n)^(-n/3))^(-6) = e^(-6) при n->беск.
так же находим предел знаменателя. Ответ, если не ошибаюсь: e^(-8) или 1/e^8.
(n-3)/(n+1) = (1-3/n) / (1+1/n).
Сводим к пределу вида (1+1/x)^x (этот предел равен е) числитель и знаменатель.
(1-3/n)^2n = ((1-3/n)^(-n/3))^(-6) = e^(-6) при n->беск.
так же находим предел знаменателя. Ответ, если не ошибаюсь: e^(-8) или 1/e^8.
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