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Консультация № 136848
14.05.2008, 20:37
0.00 руб.
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Здравствуйте. Помогите пожалуйста решить задачу: Вычислить производную функции z = x<sup>2</sup> + y в точке M(1;1) в направлении l, составляющем угол alpha=60 градусов с положительным направлением оси Ox
Обсуждение
15.05.2008, 01:40
общий
это ответ
Здравствуйте, piit!
Находим значения частных производных в точке M: дz/дx=2x, дz/дy=1, (дz/дx) (M)=2*1=2, (дz/дy) (M)=1. Находим направляющие косинусы вектора l: cos (альфа) = cos (пи/3)=1/2. sin (альфа)=sin (пи/3)=sqrt(3)/2. Следовательно, дz/дl=2*(1/2)+1*sqrt(3)/2=1+sqrt(3)/2, что приблизительно равно 1,87.
Ответ: 1+sqrt(3)/2 (приблизительно равно 1,87).
Находим значения частных производных в точке M: дz/дx=2x, дz/дy=1, (дz/дx) (M)=2*1=2, (дz/дy) (M)=1. Находим направляющие косинусы вектора l: cos (альфа) = cos (пи/3)=1/2. sin (альфа)=sin (пи/3)=sqrt(3)/2. Следовательно, дz/дl=2*(1/2)+1*sqrt(3)/2=1+sqrt(3)/2, что приблизительно равно 1,87.
Ответ: 1+sqrt(3)/2 (приблизительно равно 1,87).
Об авторе:
Facta loquuntur.
Facta loquuntur.
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