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Консультация № 197609
19.01.2020, 19:26
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1
Здравствуйте, уважаемые эксперты! У меня возникли трудности при вычислении следующих пределов:
1)
2)
3)
4)
Помогите, пожалуйста, решить эти примеры. Насчёт 1-3 возникают трудности при попытке что-то сделать с двойным факториалом. Возможно стоит использовать тот факт, что
при существовании предела справа. Но я не знаю, как это правильно применить, поэтому застреваю.
В 4 примере я так предполагаю, что можно получить что-то вида
, но также не понимаю, как это вывести (плюс проблема при упрощении привести аргумент косинуса к аргументу котангенса).
1)
2)
3)
4)
Помогите, пожалуйста, решить эти примеры. Насчёт 1-3 возникают трудности при попытке что-то сделать с двойным факториалом. Возможно стоит использовать тот факт, что
при существовании предела справа. Но я не знаю, как это правильно применить, поэтому застреваю.В 4 примере я так предполагаю, что можно получить что-то вида
, но также не понимаю, как это вывести (плюс проблема при упрощении привести аргумент косинуса к аргументу котангенса).
Обсуждение
24.01.2020, 14:25
общий
это ответ
Здравствуйте, niktrie!
К сожалению, эксперты-математики не пришли на страницу Вашей Консультации.
Чтобы хоть как-то помочь Вам в решении трудных примеров, я поручил их решение машинному вычислителю Маткад ru.wikipedia.org/wiki/Mathcad .
Маткад решил пример N4 . Для него Ответ : Предел равен 1/[$8730$]e = 0,607
Маткад-скриншот прилагаю ниже.
В 3х остальных примерах с двойным факториалом пределы возможно и не сходятся к какому-то конечному числу. Удаётся вычислить т-ко первые 2 члена. При попытке вычислить 3й член и далее число превышает допустимое для Маткада значение 10^307 .
К сожалению, эксперты-математики не пришли на страницу Вашей Консультации.
Чтобы хоть как-то помочь Вам в решении трудных примеров, я поручил их решение машинному вычислителю Маткад ru.wikipedia.org/wiki/Mathcad .
Маткад решил пример N4 . Для него Ответ : Предел равен 1/[$8730$]e = 0,607
Маткад-скриншот прилагаю ниже.
В 3х остальных примерах с двойным факториалом пределы возможно и не сходятся к какому-то конечному числу. Удаётся вычислить т-ко первые 2 члена. При попытке вычислить 3й член и далее число превышает допустимое для Маткада значение 10^307 .
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