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Консультация № 202916
23.05.2022, 16:55
0.00 руб.
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
5 вариант
Дано скалярное поле u=u(x;y):
а) составить уравнение линии уровня u=C и построить её график;
б) вычислить с помощью градиента производную скалярного поля
u=u(x;y) в точке A по направлению вектора AB
5 вариант
Дано скалярное поле u=u(x;y):
а) составить уравнение линии уровня u=C и построить её график;
б) вычислить с помощью градиента производную скалярного поля
u=u(x;y) в точке A по направлению вектора AB
Прикрепленные файлы:
Обсуждение
26.05.2022, 21:01
общий
это ответ
Здравствуйте, Anna!
Приведём уравнение
к каноническому виду, выполнив выделение полных квадратов:
Из последнего уравнения видно. что оно задаёт окружность с радиусом
и центром в точке 
Я предполагаю, что построить график такой линии уровня Вы сможете сами.
Вычислим координаты вектора
Модуль этого вектора, очевидно, равен
а направляющие косинусы -- 
(направление вектора совпадает с направлением орта оси ординат).
Дифференцируя функцию
получим
В точке
имеем
Следовательно, искомая производная
Приведём уравнение
к каноническому виду, выполнив выделение полных квадратов:Из последнего уравнения видно. что оно задаёт окружность с радиусом
и центром в точке Я предполагаю, что построить график такой линии уровня Вы сможете сами.Вычислим координаты вектора
Модуль этого вектора, очевидно, равен
а направляющие косинусы -- (направление вектора совпадает с направлением орта оси ординат).Дифференцируя функцию
получимВ точке
имеемСледовательно, искомая производная
Об авторе:
Facta loquuntur.
Facta loquuntur.
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