DHS 15.1 - Option 5. 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)

1.5. u (M) = ln (xy + yz + xz), M1 (-2, 3, -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 + y + 2z = 2

3. Calculate the surface integral of the second kind.

 where S - the upper side of the plane x + y + z = 4, severed 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.

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