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Консультация № 200561
04.04.2021, 10:11
0.00 руб.
1
4
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Прошу помочь в решении задачи:
Для функции z = 3x^4 − xy + y^3 найти:
а) производную в точке М(1,2) в направлении, составляющем с осью Ox угол в 60 градусов, а с осью Oy – тупой угол;
б) grad z в точке N(2,1).
Прошу помочь в решении задачи:
Для функции z = 3x^4 − xy + y^3 найти:
а) производную в точке М(1,2) в направлении, составляющем с осью Ox угол в 60 градусов, а с осью Oy – тупой угол;
б) grad z в точке N(2,1).
Прикрепленные файлы:
Обсуждение
04.04.2021, 13:59
общий
это ответ
Здравствуйте, Александр!
Вычислим частные производные функции
Угол в
с осью 
и тупой угол с осью 
составляет направление, задаваемое вектором 
При этом 
и
-- производная в точке
по направлению вектора 
.
Вычислим градиент функции
в точке 
-- модуль градиента.
Литература
Письменный Д. Т. Конспект лекций по высшей математике: [В 2 ч.]. Ч. 2 / Д. Т. Письменный. -- М.: Айрис-пресс, 2006. -- 256 с.
Вычислим частные производные функции
Угол в
с осью и тупой угол с осью составляет направление, задаваемое вектором При этом и-- производная в точке
по направлению вектора .Вычислим градиент функции
в точке -- модуль градиента.
Литература
Письменный Д. Т. Конспект лекций по высшей математике: [В 2 ч.]. Ч. 2 / Д. Т. Письменный. -- М.: Айрис-пресс, 2006. -- 256 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
05.04.2021, 11:34
общий
Андрей Владимирович, добрый день!
Возник вопрос про пункт а) M (x= 1, y=2) в первых двух строках, разве не так должно быть? Подставив x и y: 1) 12x^3-y = 12*1^2-2=10
2) -x+3y^2= -1+3^2=8. В ходе решение получается совсем другое. Или я не прав?
Возник вопрос про пункт а) M (x= 1, y=2) в первых двух строках, разве не так должно быть? Подставив x и y: 1) 12x^3-y = 12*1^2-2=10
2) -x+3y^2= -1+3^2=8. В ходе решение получается совсем другое. Или я не прав?
05.04.2021, 11:40
общий
05.04.2021, 15:33
Адресаты:
Прошу извинить меня! Из-за приближающейся деменции и связанной с этим невнимательностью я не заметил, что в задании указаны две разные точки. С Вашего позволения я переделаю решение вечером, когда приду домой. А сейчас мне нужно идти на занятия со студентами.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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