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Консультация № 119050
17.01.2008, 20:16
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Доброе время суток! Прошу помощи в решении. Задана функция z=f(x,y). Найти градиент и производную этой функций в заданной точке M(x0,y0) в направлении вектора l¯, составляющего угол α положительным направлением оси Ox. Z=2cos(x+y)+2x, M(π/6,π/6),α=π/3
Обсуждение
17.01.2008, 21:31
общий
это ответ
Здравствуйте, Верзаков Константин Александрович!
Градиент G = (dz/dx, dz/dy) = (-2*sin(x+y)+2, -2*sin(x+y));
После подстановки x = Pi/6, y = Pi/6 получим: G = (-sqrt(3)+2, -sqrt(3)).
Вектор Г = (cos(alpha), sin(alpha)) = (1/2, sqrt(3)/2) при alpha = Pi/3.
Чтобы найти производную в направлении Г,
перемножим скалярно векторы G и Г, получим -sqrt(3)/2 - 1/2.
Желаю успехов.
Градиент G = (dz/dx, dz/dy) = (-2*sin(x+y)+2, -2*sin(x+y));
После подстановки x = Pi/6, y = Pi/6 получим: G = (-sqrt(3)+2, -sqrt(3)).
Вектор Г = (cos(alpha), sin(alpha)) = (1/2, sqrt(3)/2) при alpha = Pi/3.
Чтобы найти производную в направлении Г,
перемножим скалярно векторы G и Г, получим -sqrt(3)/2 - 1/2.
Желаю успехов.
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