DHS 15.1 - Option 18. 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)

1.18. u (M) = xy - 3xyz, M1 (2, 2, -4), M2 (1, 0, -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 surface of the paraboloid z = 3 - x2 - y2 (normal vector n which forms an acute angle with the unit vector k), cut-off plane z = 0.

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.

4.18. and (M) = (x + y + z) i + 2zj + (y - 7z) k, (p): 2x + 3y + z = 6