DHS 15.1 - Option 7. 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)

1.7. u (M) = x2y + xz2 - 2, M1 (1, 1, -1), M2 (2, 1, 3)

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): 2x - 3y + z = 6

3. Calculate the surface integral of the second kind.

 where S - the outer side of the sphere x2 + y2 + z2 = 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.

4.7. and (M) = (3x - y) i + (2y + z) j + (2z - x) k, (p): 2x - 3y + z = 6