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Консультация № 184041
16.09.2011, 23:50
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
1)Разложить функцию в ряд Маклорена,определить область сходимости ряда а)f(x)=3cos(3x^2),б)f(x)=3/(4-3x^2) Огромное спасибо!!!!!!!!!!!!
1)Разложить функцию в ряд Маклорена,определить область сходимости ряда а)f(x)=3cos(3x^2),б)f(x)=3/(4-3x^2) Огромное спасибо!!!!!!!!!!!!
Обсуждение
Неизвестный
17.09.2011, 02:20
общий
это ответ
Здравствуйте, леди!
а)
т.к.
тогда
Данный ряд сходится при
а)
т.к.
тогда
Данный ряд сходится при
17.09.2011, 09:04
общий
это ответ
Здравствуйте, леди!
б) f(x)=(3/4)*1/(1-(3x2/4))
По формуле суммы геометрической прогрессии
f(x)=(3/4)*[$8721$]n=0[$8734$](3x2/4)n=[$8721$]n=0[$8734$](3n+1/4n+1)x2n
Условие сходимости ряда |3x2/4)|<1, т.е. |x|<2/[$8730$]3
Область сходимости - интервал (-2/[$8730$]3;2/[$8730$]3)
б) f(x)=(3/4)*1/(1-(3x2/4))
По формуле суммы геометрической прогрессии
f(x)=(3/4)*[$8721$]n=0[$8734$](3x2/4)n=[$8721$]n=0[$8734$](3n+1/4n+1)x2n
Условие сходимости ряда |3x2/4)|<1, т.е. |x|<2/[$8730$]3
Область сходимости - интервал (-2/[$8730$]3;2/[$8730$]3)
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