DHS 15.1 - Option 25. Decisions Ryabushko AP
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$1.3
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)
1.25. u (M) = 10 / (x2 + y2 + z2 + 1), M1 (-1, 2, -2), M2 (2, 0, 1)
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 + 3z = 6
3. Calculate the surface integral of the second kind.
where S - the surface of the paraboloid 9 - z = 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.
4.25. and (M) = (y + z) i + (2x - z) j + (y + 3z) k, (p): 2x + y + 3z = 6
1.25. u (M) = 10 / (x2 + y2 + z2 + 1), M1 (-1, 2, -2), M2 (2, 0, 1)
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 + 3z = 6
3. Calculate the surface integral of the second kind.
where S - the surface of the paraboloid 9 - z = 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.
4.25. and (M) = (y + z) i + (2x - z) j + (y + 3z) k, (p): 2x + y + 3z = 6
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