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DHS 15.1 - Option 15. Decisions Ryabushko AP
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Uploaded: 17.01.2024
Content: 15v-IDZ15.1.doc 274,5 kB
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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)
1.15. u (M) = x2 + 2y2 - 4z2 - 5, M1 (1, 2, 1), M2 (-3, -2, 6)
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 + 4y + 2z = 8
3. Calculate the surface integral of the second kind.
where S - the outer side of the sphere x2 + y2 + z2 = 1 lying in the first octant
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.
4.15. and (M) = (2z - x) i + (x + 2y) j + 3zk, (p): x + 4y + 2z = 8
Additional information
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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