DHS 15.1 - Option 21. 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)

1.21. u (M) = xyz, M1 (3, 1, 4), M2 (1, -1, -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 + 2z = 4

3. Calculate the surface integral of the second kind.

 where S - the inner side of the cylinder x2 + y2 = 4, cut off by the plane z = 0 and z = 1

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.

4.21. and (M) = (2z - x) i + (x - y) j + (3x + z) k, (p): x + y + 2z = 2