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Консультация № 199897
16.12.2020, 12:28
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Применяя формулу Тейлора с остаточным членом в форме Лагранжа к функции f(x)=e^x вычислить значение e^a с точностью 0.001, а=0.78
Применяя формулу Тейлора с остаточным членом в форме Лагранжа к функции f(x)=e^x вычислить значение e^a с точностью 0.001, а=0.78
Обсуждение
22.12.2020, 05:08
общий
это ответ
Здравствуйте, werevolf1!
Для произвольной функции f(x) формула Тейлора с остаточным членом в форме Лагранжа имеет вид:
где x[sub]0[/sub] < c < x. В данном случае для f(x) = e[sup]x[/sup] и x[sub]0[/sub] = 0 f[sup](k)[/sup](x) = e[sup]x[/sup], f[sup](k)[/sup](0) = 1 для всех k и
В частности, для a = 0.78 разложение
гарантирует точность 0.001, так как при любом 0 < c < 0.78
Соответственно,
что отличается от точного значения e[sup]0.78[/sup] = 2.1814722655 менее, чем на 0.0005.
Для произвольной функции f(x) формула Тейлора с остаточным членом в форме Лагранжа имеет вид:
где x[sub]0[/sub] < c < x. В данном случае для f(x) = e[sup]x[/sup] и x[sub]0[/sub] = 0 f[sup](k)[/sup](x) = e[sup]x[/sup], f[sup](k)[/sup](0) = 1 для всех k и
В частности, для a = 0.78 разложение
гарантирует точность 0.001, так как при любом 0 < c < 0.78
Соответственно,
что отличается от точного значения e[sup]0.78[/sup] = 2.1814722655 менее, чем на 0.0005.
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