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Консультация № 132284
15.04.2008, 11:04
0.00 руб.
0
1
1
Помогите решить задачу.
Даны функция z=(x;y), точка A(x0;y0) и вектор a. Найти
1) grad z в точке А;
2) производную в точке А по направлению вектора а.
z=2x^2 + 3 xy +y^2; A(2;1), a=3i-4j.
Даны функция z=(x;y), точка A(x0;y0) и вектор a. Найти
1) grad z в точке А;
2) производную в точке А по направлению вектора а.
z=2x^2 + 3 xy +y^2; A(2;1), a=3i-4j.
Обсуждение
Неизвестный
15.04.2008, 11:22
общий
это ответ
Здравствуйте, Kiselev!
1) grad z=dz/dx*i+dz/dy*j
dz/dx=4x+3y
dz/dx(A)=4*2+3*1=8+3=11
dz/dy=3x+2y
dz/dy(A)=3*2+2*1=6+2=8
grad z=(4x+3y)*i+(3x+2y)*j
grad z(A)=11*i+8*j
2) Для нахождения производной по направлению вектора а в точке А перемножим скалярно grad z(A) и a:
(a,grad z)(A)=3*11+(-4)*8=33-32=1
1) grad z=dz/dx*i+dz/dy*j
dz/dx=4x+3y
dz/dx(A)=4*2+3*1=8+3=11
dz/dy=3x+2y
dz/dy(A)=3*2+2*1=6+2=8
grad z=(4x+3y)*i+(3x+2y)*j
grad z(A)=11*i+8*j
2) Для нахождения производной по направлению вектора а в точке А перемножим скалярно grad z(A) и a:
(a,grad z)(A)=3*11+(-4)*8=33-32=1
Форма ответа
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