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Консультация № 67023
14.12.2006, 21:57
0.00 руб.
0
3
2
здравствуйте,уважаемые эксперты.Помогите пожалуйста решить пример.Я ООООчень вас прошу!
Вычислить предел при Х,стремящемся к 3 для функции (lnx-ln3)/(x-3).
Вычислить предел при Х,стремящемся к 3 для функции (lnx-ln3)/(x-3).
Обсуждение
Неизвестный
14.12.2006, 22:08
общий
это ответ
Здравствуйте, Янусик!
Используем правило Лопиталя, получаем (1/x)/1 при x->3, то есть (1/3)/1, то есть просто 1/3.
Используем правило Лопиталя, получаем (1/x)/1 при x->3, то есть (1/3)/1, то есть просто 1/3.
Неизвестный
15.12.2006, 15:32
общий
это ответ
Здравствуйте, Янусик!
Есть несколько способв (в зависимости от того, какой нужно использовать):
1) lnx - ln3 = ln(x/3) далее по формуле Тейлора
ln(x/3) = 1/3(x-3) + o((x-3)^2) (степень в о малом точно не помню, может и 1)
2) по правилу Лопиталя (этот способ уже рассматривался другим экспертом). Иногда преподы говорят найти предел другим способом, поэтому и привожу их.
3) замечательный предел
lnx-ln3 = ln(1 + (x/3 - 1));
x-3 = 3 * (x/3 - 1)
Вот сам замечательный предел: lim(a->0) ln(1+a)/a = 1.
Есть несколько способв (в зависимости от того, какой нужно использовать):
1) lnx - ln3 = ln(x/3) далее по формуле Тейлора
ln(x/3) = 1/3(x-3) + o((x-3)^2) (степень в о малом точно не помню, может и 1)
2) по правилу Лопиталя (этот способ уже рассматривался другим экспертом). Иногда преподы говорят найти предел другим способом, поэтому и привожу их.
3) замечательный предел
lnx-ln3 = ln(1 + (x/3 - 1));
x-3 = 3 * (x/3 - 1)
Вот сам замечательный предел: lim(a->0) ln(1+a)/a = 1.
Форма ответа
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