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Консультация № 194243
19.12.2018, 16:01
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить выражение пользуясь правилами подсчета цифр. Определить абсолютную погрешность результата, предполагая, что все цифры данных чисел являются верными значащими цифрами. Выражение в прикрепленном файле.
Вычислить выражение пользуясь правилами подсчета цифр. Определить абсолютную погрешность результата, предполагая, что все цифры данных чисел являются верными значащими цифрами. Выражение в прикрепленном файле.
Прикрепленные файлы:
Обсуждение
22.12.2018, 16:02
общий
это ответ
Здравствуйте, alexey.kravtsov95!
Воспользуемся следующими правилами:
Тогда
Предположим, что в заданных числах все цифры являются верными в узком смысле, то есть абсолютная погрешность каждого числа не превышает половины единицы разряда, выражаемого последней цифрой, считая слева направо. Тогда
Преобразуем заданное выражение, чтобы упростить дифференцирование, следующим образом:
Дифференцируя это выражение как функцию от величин
получим
Вычислим значения частных производных; получим (округляя конечные результаты с избытком)
Вычислим предельную абсолютную погрешность; получим
Результат вычислений можно записать так:
Литература. Лабораторные работы по курсу "Высшая математика" для технических специальностей. Часть I. / С. Т. Гусева, А. В. Санюкевич. - Брест: Брестский государственный технический университет, 2003. - 51 с.
Воспользуемся следующими правилами:
Тогда
Предположим, что в заданных числах все цифры являются верными в узком смысле, то есть абсолютная погрешность каждого числа не превышает половины единицы разряда, выражаемого последней цифрой, считая слева направо. Тогда
Преобразуем заданное выражение, чтобы упростить дифференцирование, следующим образом:
Дифференцируя это выражение как функцию от величин
получимВычислим значения частных производных; получим (округляя конечные результаты с избытком)
Вычислим предельную абсолютную погрешность; получим
Результат вычислений можно записать так:
Литература. Лабораторные работы по курсу "Высшая математика" для технических специальностей. Часть I. / С. Т. Гусева, А. В. Санюкевич. - Брест: Брестский государственный технический университет, 2003. - 51 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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