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Консультация № 185251
22.01.2012, 13:21
52.91 руб.
0
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Здравствуйте! Прошу помощи в следующем вопросе:
Применив формулу Тейлора с остаточным членом в форме Лагранжа к функции f(x)=e^x, вычислить с абсолютной погрешностью [$916$]=0,001 значения e^a и e^b
a=0,23
b=0,26
Применив формулу Тейлора с остаточным членом в форме Лагранжа к функции f(x)=e^x, вычислить с абсолютной погрешностью [$916$]=0,001 значения e^a и e^b
a=0,23
b=0,26
Обсуждение
22.01.2012, 14:57
общий
это ответ
Здравствуйте, Максим!
Все производные e^x в точке 0 равны 1.
Формула Тейлора имеет вид e^x=1+x+x^2/2!+...x^n/n!+e^[$952$]x x^(n+1)/(n+1)!
Погрешность оценивается как 0<rn(x)<e^x x^(n+1)/(n+1)!<3 x^(n+1)/(n+1)!
Абсолютная погрешность будет меньше [$916$]=0,001, если следующих член меньше [$916$]/3
Поскольку вручную считать трудно, воспользуемся программой Excel. скачать файл 251.xlsx [8.6 кб]
e^a=1,258594434
e^b=1,29691974
Все производные e^x в точке 0 равны 1.
Формула Тейлора имеет вид e^x=1+x+x^2/2!+...x^n/n!+e^[$952$]x x^(n+1)/(n+1)!
Погрешность оценивается как 0<rn(x)<e^x x^(n+1)/(n+1)!<3 x^(n+1)/(n+1)!
Абсолютная погрешность будет меньше [$916$]=0,001, если следующих член меньше [$916$]/3
Поскольку вручную считать трудно, воспользуемся программой Excel. скачать файл 251.xlsx [8.6 кб]
e^a=1,258594434
e^b=1,29691974
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