DHS 15.1 - Option 22. 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)

1.22. u (M) = (x2 + y2 + z2) 3, M1 (1, 2, -1), M2 (0, 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 + 2z = 2

3. Calculate the surface integral of the second kind.

 where S - the outer side of the closed surface formed by a paraboloid 3z = x2 + y2 and hemisphere z = √4 - x2 - y2.

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.

4.22. and (M) = (x + z) i + (x + 3y) j + yk, (p): x + y + 2z = 2