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Консультация № 150376
12.11.2008, 23:14
0.00 руб.
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Нужна помощь с решением пары примеров по мат.анализу 1...1) lim при x -> Пи/2 cosx делить на (1-sinx)^1/32) lim при x->+0 1-(cosx)^1/2 делить на 1-cos корень из x.....Помогите,погибаю
Приложение:
знак ^ имеет значение возведения предыдущего выражения в степень
Обсуждение
14.11.2008, 07:07
общий
Примеры с небольшой хитростью. Применять правило Лопиталя сходу кажется, что не получается. На самом деле это не так. Истоки использования этого правила в том, что если две разные функции разложимы в ряд Тейлора в окрестности точки, то даже если первые несколько членов у них одинаковы, все равно какие-то отличаются. Так что предел отношения этих функций будет равен отношению этих членов. Значит надо "подготовить" пример для применения этого правила.
В первом примере нужно искать корень третьей степени из лимита выражения в кубе (кто нам мешает?). Тогда применяем правило Лопиталя два раза и получаем предел 0.
Во втором примере сразу используем правило Лопиталя один раз, но потом останавливаемся и смотрим на выражение. В знаменателе стоит 1-й замечательный предел, только относительно корня из х, который равен 1 (еще коэффициент). А в числителе 0, значит общий предел 0.
В первом примере нужно искать корень третьей степени из лимита выражения в кубе (кто нам мешает?). Тогда применяем правило Лопиталя два раза и получаем предел 0.
Во втором примере сразу используем правило Лопиталя один раз, но потом останавливаемся и смотрим на выражение. В знаменателе стоит 1-й замечательный предел, только относительно корня из х, который равен 1 (еще коэффициент). А в числителе 0, значит общий предел 0.
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