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Консультация № 188556
26.12.2015, 21:28
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Рельеф местности в пределах некоторого географического района может быть описан приближенно функцией z = f (x, у). Направление grad z в точке A(x0, y0) определяет направление линии наиболее крутого ската в данной точке, а величина |grad z| – крутизну этого ската.
1. Найти grad z в точке А.
2. Оценить характер (возвышенность или низменность) и скорость изменения рельефа данной местности в точке А в направлении, определяемом вектором
a = 4i - 3 j .
3. Записать уравнение касательной плоскости и нормали к поверхности z=f(x,y) в данной точке А.
Функция z = f (x, у) и координаты точки А даны в ниже
Z - 3х^2 +10ху+3у^2 –12x–12y+7
A - (1, 3)
Рельеф местности в пределах некоторого географического района может быть описан приближенно функцией z = f (x, у). Направление grad z в точке A(x0, y0) определяет направление линии наиболее крутого ската в данной точке, а величина |grad z| – крутизну этого ската.
1. Найти grad z в точке А.
2. Оценить характер (возвышенность или низменность) и скорость изменения рельефа данной местности в точке А в направлении, определяемом вектором
a = 4i - 3 j .
3. Записать уравнение касательной плоскости и нормали к поверхности z=f(x,y) в данной точке А.
Функция z = f (x, у) и координаты точки А даны в ниже
Z - 3х^2 +10ху+3у^2 –12x–12y+7
A - (1, 3)
Обсуждение
27.12.2015, 10:12
общий
это ответ
Здравствуйте, bissinbeev!
1. Находим направление и величину вектора градиента
в точке 
2. Находим скорость изменения рельефа данной местности в точке
в направлении, определяемом вектором 
- направляющие косинусы вектора
- производная по направлению
вектора
Из полученных результатов видно, что функция
(высота местности) возрастает в направлении векторов градиента и 
По-видимому, местность является возвышенностью.
3. Записываем уравнения
- касательной плоскости к поверхности в точке
- нормали к поверхности в точке
Обязательно проверьте выкладки во избежание ошибок!
С уважением.
1. Находим направление и величину вектора градиента
в точке 2. Находим скорость изменения рельефа данной местности в точке
в направлении, определяемом вектором - направляющие косинусы вектора
- производная по направлению
вектора Из полученных результатов видно, что функция
(высота местности) возрастает в направлении векторов градиента и По-видимому, местность является возвышенностью.3. Записываем уравнения
- касательной плоскости к поверхности в точке
- нормали к поверхности в точке
Обязательно проверьте выкладки во избежание ошибок!
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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