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Консультация № 174962
07.12.2009, 00:46
0.00 руб.
0
2
2
Здравствуйте, Уважаемые эксперты.
Помогите, пожалуйста, в решении следующей задачи.
Разложить функцию в ряд Тейлора по степеням x-x0
y=e^(x/a) , x0=a
Помогите, пожалуйста, в решении следующей задачи.
Разложить функцию в ряд Тейлора по степеням x-x0
y=e^(x/a) , x0=a
Обсуждение
Неизвестный
07.12.2009, 15:52
общий
это ответ
Здравствуйте, filins.
y = e^(x/a) = e^(x0/a) + (1/a)*e^(x0/a)*(x-x0)/1! + (1/a^2)*e^(x0/a)*(x-x0)^2/2! + (1/a^3)*e^(x0/a)*(x-x0)^3/3! + . . . +
+ (1/a^n)*e^(x0/a)*(x-x0)^n/n! + . . . = e*[1 + (1/a)*(x-a)/1! + (1/a^2)*(x-a)^2/2! + (1/a^3)*(x-a)^3/3! + . . . +
+ (1/a^n)*(x-a)^n/n! + . . .
n -> ∞
y = e^(x/a) = e^(x0/a) + (1/a)*e^(x0/a)*(x-x0)/1! + (1/a^2)*e^(x0/a)*(x-x0)^2/2! + (1/a^3)*e^(x0/a)*(x-x0)^3/3! + . . . +
+ (1/a^n)*e^(x0/a)*(x-x0)^n/n! + . . . = e*[1 + (1/a)*(x-a)/1! + (1/a^2)*(x-a)^2/2! + (1/a^3)*(x-a)^3/3! + . . . +
+ (1/a^n)*(x-a)^n/n! + . . .
n -> ∞
5
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