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Консультация № 194479
20.01.2019, 17:57
0.00 руб.
0
2
1
Здравствуйте! Прошу помощи в следующем вопросе:
Определить порядок
o(x)= (1+2x)^1/2 - 1-x-(x^3)^1/2
относительно х
а) при
x ->0
б)при
x ->бесконечности
Можно по подробнее, пожалуйста, даже не знаю с чего начать
Определить порядок
o(x)= (1+2x)^1/2 - 1-x-(x^3)^1/2
относительно х
а) при
x ->0
б)при
x ->бесконечности
Можно по подробнее, пожалуйста, даже не знаю с чего начать
Обсуждение
23.01.2019, 17:10
общий
это ответ
Здравствуйте, ms.any2000!
а) Пусть
Тогда
Значит, заданная функция при
является бесконечно малой величиной высшего порядка, чем 
Здесь при вычислении предела мы воспользовались тем, что при 
Это доказывается, например, Г. М. Фихтенгольцем в первом томе его "Курса дифференциального и интегрального исчисления".
б) Пусть
Тогда
Значит, заданная функция при
является бесконечно большой величиной высшего порядка, чем
а) Пусть
ТогдаЗначит, заданная функция при
является бесконечно малой величиной высшего порядка, чем Здесь при вычислении предела мы воспользовались тем, что при Это доказывается, например, Г. М. Фихтенгольцем в первом томе его "Курса дифференциального и интегрального исчисления".б) Пусть
ТогдаЗначит, заданная функция при
является бесконечно большой величиной высшего порядка, чем
Об авторе:
Facta loquuntur.
Facta loquuntur.
23.01.2019, 17:11
общий
Я отправил ответ на 48 минут раньше разрешённого мне срока, потому что в ближайшее время ко мне домой должен придти монтажник из телефонной станции для изменения подключения телефонной линии, в связи с чем я могу быть лишён возможности выхода в Интернет.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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