**Content:** 4v-IDZ15.1.doc (204.00 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)

1.4. u (M) = zex2 + y2 + z2, M1 (0, 0, 0), M2 (3, -4, 2)

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 + z = 2

3. Calculate the surface integral of the second kind.

where S - the outer side surface of the sphere x2 + y2 + z2 = 16

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.

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

1.4. u (M) = zex2 + y2 + z2, M1 (0, 0, 0), M2 (3, -4, 2)

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 + z = 2

3. Calculate the surface integral of the second kind.

where S - the outer side surface of the sphere x2 + y2 + z2 = 16

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.

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

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

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