DHS 15.1 - Option 2. 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)

1.2. u (M) = 5xy3z2, M1 (2, 1, -1), M2 (4, -3, 0)

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 outer side surface of the ellipsoid x2 + y2 + 2z2 = 2

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.

4.2. and (M) = (3x - 1) i + (y - x + z) j + 4zk, (p): 2x - y - 2z = 2