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Консультация № 186280
01.06.2012, 14:11
129.44 руб.
0
2
2
Здравствуйте! Прошу помощи в следующем вопросе:
Решите пожалуйста мои задания :)
Решите пожалуйста мои задания :)
Обсуждение
01.06.2012, 14:35
общий
это ответ
Здравствуйте, Посетитель - 393715!
2.
Косинус голоморфен всюду на комплексной плоскости. Значит надо проверить лишь бесконечность.
,
если z действительно.
И косинус неограничен при z чисто мнимом, т.к.
.
Так что бесконечность - существенно особая точка.
2.
Косинус голоморфен всюду на комплексной плоскости. Значит надо проверить лишь бесконечность.
,если z действительно.
И косинус неограничен при z чисто мнимом, т.к.
.Так что бесконечность - существенно особая точка.
01.06.2012, 15:43
общий
это ответ
Здравствуйте, Посетитель - 393715!
1. Пусть требуется вычислить интеграл
представив его, как указано в задании, в цилиндрических координатах.
Рассмотрим сначала, что представляет собой проекция области интегрирования на плоскость
Из выражения для верхнего предела интегрирования по переменной 
получим
т. е. уравнение окружности радиуса
с центром в точке 
Проекция области интегрирования на рассмотренную плоскость - верхний полукруг, ограниченный этой окружностью.
Положим
Тогда
Если принять
за абсциссу, - за ординату, 
за аппликату точки пространства, то область интегрирования - полуцилиндр, ограниченный снизу плоскостью 
сверху плоскостью 
спереди - плоскостью 
Радиус цилиндра 
а центр основания находится в точке 
Переходя к цилиндрическим координатам, получим
С уважением.
1. Пусть требуется вычислить интеграл
представив его, как указано в задании, в цилиндрических координатах.
Рассмотрим сначала, что представляет собой проекция области интегрирования на плоскость
Из выражения для верхнего предела интегрирования по переменной получимт. е. уравнение окружности радиуса
с центром в точке Проекция области интегрирования на рассмотренную плоскость - верхний полукруг, ограниченный этой окружностью.Положим
ТогдаЕсли принять
за абсциссу, - за ординату, за аппликату точки пространства, то область интегрирования - полуцилиндр, ограниченный снизу плоскостью сверху плоскостью спереди - плоскостью Радиус цилиндра а центр основания находится в точке Переходя к цилиндрическим координатам, получим
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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