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Консультация № 173872
01.11.2009, 10:15
0.00 руб.
0
2
1
Доброго времени суток, коллеги. Помогите сориентироваться - хотя бы от чего отталкиваться при решении.
limx[$8594$]0[ln(1-x2)/x]
Ответ (или совет) нужен сегодня.
Заранее спасибо всем откликнувшимся
limx[$8594$]0[ln(1-x2)/x]
Ответ (или совет) нужен сегодня.
Заранее спасибо всем откликнувшимся
Обсуждение
Неизвестный
01.11.2009, 11:06
общий
это ответ
Здравствуйте, Botsman.
limx[$8594$]0[ln(1-x2)/x] = -limx[$8594$]0[ln(1-x2)/(-x2) * x] = -limx[$8594$]0[ln(1-x2)/(-x2)] * limx[$8594$]0[x] = {-x2 = t} = -limt[$8594$]0[ln(1+t)/t] * limx[$8594$]0[x] = -1*0 = 0.
P.S.
limt[$8594$]0[ln(1+t)/t] = 1. Это является следствием второго замечательного предела.
limx[$8594$]0[ln(1-x2)/x] = -limx[$8594$]0[ln(1-x2)/(-x2) * x] = -limx[$8594$]0[ln(1-x2)/(-x2)] * limx[$8594$]0[x] = {-x2 = t} = -limt[$8594$]0[ln(1+t)/t] * limx[$8594$]0[x] = -1*0 = 0.
P.S.
limt[$8594$]0[ln(1+t)/t] = 1. Это является следствием второго замечательного предела.
5
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