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Консультация № 188547
24.12.2015, 22:53
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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,y).Направление grad z в точке A(x0,y0) определяет направление линии наиболее крутого ската в данной точке, а величина |grad z|-крутизна этого ската.
1.Найти grad z в точке A
2.Оценить характер (возвышенность или низменность) и скорость изменения рельефная данной местности в точке A в направлении, определением вектор a = 4 вектор i - 3 вектор i.
3. Записать уравнение касательной плоскости и нормали к поверхности z=f(x,y) в данной точке A.
z=5x^2 -4xy+2y^2+10x+10y+6,5
A(1,-0,5)
Рельеф местности в пределах некоторого географического района может быть описан приближенно функцией z=f(x,y).Направление grad z в точке A(x0,y0) определяет направление линии наиболее крутого ската в данной точке, а величина |grad z|-крутизна этого ската.
1.Найти grad z в точке A
2.Оценить характер (возвышенность или низменность) и скорость изменения рельефная данной местности в точке A в направлении, определением вектор a = 4 вектор i - 3 вектор i.
3. Записать уравнение касательной плоскости и нормали к поверхности z=f(x,y) в данной точке A.
z=5x^2 -4xy+2y^2+10x+10y+6,5
A(1,-0,5)
Обсуждение
25.12.2015, 09:33
общий
это ответ
Здравствуйте, urazlyaev!
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
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
Проверьте выкладки во избежание ошибок.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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