**Content:** 7v-IDZ15.1.doc (253.50 KB)

**Uploaded:** 09.11.2016

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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)

1.7. u (M) = x2y + xz2 - 2, M1 (1, 1, -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 - 3y + z = 6

3. Calculate the surface integral of the second kind.

where S - the outer side of the sphere x2 + y2 + z2 = 1

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.

4.7. and (M) = (3x - y) i + (2y + z) j + (2z - x) k, (p): 2x - 3y + z = 6

1.7. u (M) = x2y + xz2 - 2, M1 (1, 1, -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 - 3y + z = 6

3. Calculate the surface integral of the second kind.

where S - the outer side of the sphere x2 + y2 + z2 = 1

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.

4.7. and (M) = (3x - y) i + (2y + z) j + (2z - x) k, (p): 2x - 3y + z = 6

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)

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