DHS 15.1 - Option 24. 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)

1.24. u (M) = x2y + y2z - 3z, M1 (0, -2, -1), M2 (12, -5, 0)

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 cylinder x2 + y2 = 1, cut off by the plane z = 0 and z = 2

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.

4.24. and (M) = (3x + y) i + (x + z) j + yk, (p): x + 2y + z = 2