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Консультация № 176718
17.02.2010, 10:23
42.08 руб.
0
4
3
Здравствуйте решите пожалуйста задание желательно по подробней(хотя бы в 2-3действия).
Вычислить предел :
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Обсуждение
Неизвестный
17.02.2010, 10:38
общий
17.02.2010, 11:33
это ответ
Здравствуйте, kapezc.
Этот предел равен 4.
Решение оформлю картинкой и вставлю в мини-форум к этому вопросу, так как в ответы вставлять картинки не умею.
Этот предел равен 4.
Решение оформлю картинкой и вставлю в мини-форум к этому вопросу, так как в ответы вставлять картинки не умею.
5
Неизвестный
17.02.2010, 12:38
общий
17.02.2010, 13:01
это ответ
Здравствуйте, kapezc!
Lim = 4, так как это предел 0/0, то по теореме Лопиталя, берем производную делителя и делимого и рассматриваем этот предел, т.е. Lim x->0 (-sinX + 3*sin3X) / (2X + 3X^2), далее при x->0 sinX=X, получаем Lim x->0 (-X+3*3X)/ (2X+3X^2)= Lim x->0 (8X)/ (X*(2+3X)) = Lim x->0 8/ (2+3X) = 8/2 = 4
Lim = 4, так как это предел 0/0, то по теореме Лопиталя, берем производную делителя и делимого и рассматриваем этот предел, т.е. Lim x->0 (-sinX + 3*sin3X) / (2X + 3X^2), далее при x->0 sinX=X, получаем Lim x->0 (-X+3*3X)/ (2X+3X^2)= Lim x->0 (8X)/ (X*(2+3X)) = Lim x->0 8/ (2+3X) = 8/2 = 4
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