ИДЗ 15.1 – Вариант 15. Решения Рябушко А.П.

1. Dana function u (M) = u (x, y, z) and the point M1, M2. Calculate: 1) The derivative of this function in the direction of the point M1 M1M2 vector; 2) grad u (M1)

1.15. u (M) = x2 + 2y2 - 4z2 - 5, M1 (1, 2, 1), M2 (-3, -2, 6)

2. Calculate the surface integral of the first kind on the surface S, where S - part of the plane (p), cut off by the coordinate planes.

 (P): x + 4y + 2z = 8

3. Calculate the surface integral of the second kind.

 where S - the outer side of the sphere x2 + y2 + z2 = 1 lying in the first octant

4. Calculate the flow vector field a (M) through the outer surface of the pyramid formed by plane (p) and the coordinate planes in two ways: a) determination using flow; b) using the formula Ostrogradskii - Gauss.

4.15. and (M) = (2z - x) i + (x + 2y) j + 3zk, (p): x + 4y + 2z = 8

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