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Консультация № 186900
04.12.2012, 15:49
78.80 руб.
04.12.2012, 20:10
0
8
2
Здравствуйте! У меня возникли сложности с таким вопросом:
найти предел при х стремящемся к нулю: (x*x*ctg(2x))/ sin(3x)
найти предел при х стремящемся к нулю: (x*x*ctg(2x))/ sin(3x)
Обсуждение
04.12.2012, 16:06
общий
это ответ
Здравствуйте, Марина!
Здесь использовалась эквивалентность бесконечно малых величин sin[$945$]~[$945$], tg[$945$]~[$945$] при [$945$][$8594$]0.
Здесь использовалась эквивалентность бесконечно малых величин sin[$945$]~[$945$], tg[$945$]~[$945$] при [$945$][$8594$]0.
04.12.2012, 16:41
общий
04.12.2012, 16:42
Адресаты:
Разве 
- бесконечно малая величина?! И что значит величина 
?
- бесконечно малая величина?! И что значит величина ?
Об авторе:
Facta loquuntur.
Facta loquuntur.
04.12.2012, 16:44
общий
Вы правильно записали условие? Может быть, должно быть не 
а 
?
а ?
Об авторе:
Facta loquuntur.
Facta loquuntur.
04.12.2012, 19:34
общий
Адресаты:
Да, Вы правы, решение записано с ошибкой. Оно записано для случая, когда х[$8594$]0.
04.12.2012, 20:24
общий
Адресаты:
Благодарю за напоминание.
Я как-то не заметила, что оказывается теперь у меня есть возможность редактировать свой ответ.
Я как-то не заметила, что оказывается теперь у меня есть возможность редактировать свой ответ.
06.12.2012, 02:17
общий
это ответ
Здравствуйте, Марина!
Задачу можно решить и другим способом, используя так называемый первый замечательный предел
. Тогда 
и
И, наконец, можно (хотя в данном случае в этом нет необходимости) применить правило раскрытия неопределённостей, которое приписывают Гийому де Лопиталю, несмотря на то, что он узнал его из переписки с Иоганном Бернулли. Это правило заключается в замене отношения функций отношением производных этих функций. В нашем случае получим:
С уважением.
Задачу можно решить и другим способом, используя так называемый первый замечательный предел
. Тогда иИ, наконец, можно (хотя в данном случае в этом нет необходимости) применить правило раскрытия неопределённостей, которое приписывают Гийому де Лопиталю, несмотря на то, что он узнал его из переписки с Иоганном Бернулли. Это правило заключается в замене отношения функций отношением производных этих функций. В нашем случае получим:
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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