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Консультация № 195908
27.06.2019, 18:00
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить корень нелинейного уравнения методом касательных с заданной погрешностью вычисления = 0,001. Интервал изоляции корня указан в квадратных скобках.
Вычислить корень нелинейного уравнения методом касательных с заданной погрешностью вычисления = 0,001. Интервал изоляции корня указан в квадратных скобках.
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Обсуждение
30.06.2019, 08:31
общий
это ответ
Здравствуйте, Adelina!
Вычислим производные
Исследуем знаки второй производной на заданном отрезке. Для этого приравняем вторую производную к нулю и решим полученное уравнение относительно
из графика в прикреплённом файле видно, что
При этом
Следовательно, левее точки
вторая производная на заданном отрезке отрицательна, а правее -- положительна.
Поскольку на концах отрезка
постольку на отрезке
функция 
возрастает, поэтому в соответствии с указанием на странице 47 и рисунком 2.7, c [1] проводим касательную в точке 
Определим точку 
пересечения этой касательной с осью 
При этом
поэтому новую касательную проведём в точке
Определим точку пересечения 
этой касательной с осью
При этом
поэтому новую касательную проведём в точке
Определим точку пересечения 
этой касательной с осью
Имеем
поэтому дальнейшее уточнение корня уравнения не требуется. Ответом к заданию является 
Литература
1. Плотников А. Д. Численные методы. -- Минск: Новое знание, 2007. -- 174 с.
Вычислим производные
Исследуем знаки второй производной на заданном отрезке. Для этого приравняем вторую производную к нулю и решим полученное уравнение относительно
из графика в прикреплённом файле видно, что
При этомСледовательно, левее точки
вторая производная на заданном отрезке отрицательна, а правее -- положительна.Поскольку на концах отрезка
постольку на отрезке
функция возрастает, поэтому в соответствии с указанием на странице 47 и рисунком 2.7, c [1] проводим касательную в точке Определим точку пересечения этой касательной с осью При этом
поэтому новую касательную проведём в точке
Определим точку пересечения этой касательной с осью При этом
поэтому новую касательную проведём в точке
Определим точку пересечения этой касательной с осью Имеем
поэтому дальнейшее уточнение корня уравнения не требуется. Ответом к заданию является Литература
1. Плотников А. Д. Численные методы. -- Минск: Новое знание, 2007. -- 174 с.
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Об авторе:
Facta loquuntur.
Facta loquuntur.
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