DHS 15.1 - Option 8. 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)

1.8. u (M) = xey + yex - z2, M1 (3, 0, 2), M2 (4, 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): x - y + z = 2

3. Calculate the surface integral of the second kind.

 where S - the upper part of the plane x + y + z = 1, cut off the coordinate planes

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.

4.8. and (M) = (2y + z) i + (x - y) j - 2zk, (p): x - y + z = 2