DHS 15.1 - Option 6. Decisions Ryabushko AP

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)

1.6. u (M) = √1 + x2 + y2 + z2, M1 (1, 1, 1), M2 (3, 2, 1)

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 + 2y + z = 2

3. Calculate the surface integral of the second kind.

 where S - the outer side of the sphere x2 + y2 + z2 = 16, which lies 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.

4.6. and (M) = (x + z) i + 2yj + (x + y - z) k, (p): x + 2y + z = 2