**Content:** 20v-IDZ15.1.doc (226.50 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)

1.20. u (M) = exy + z2, M1 (-5, 0, 2), M2 (2, 4, -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 surface of the paraboloid z = x2 + y2 (normal vector n which forms an acute angle with the unit vector k), cut-off plane z = 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.

4.20. and (M) = (2y - z) i + (x + y) j + xk, (p): x + 2y + 2z = 4

1.20. u (M) = exy + z2, M1 (-5, 0, 2), M2 (2, 4, -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 surface of the paraboloid z = x2 + y2 (normal vector n which forms an acute angle with the unit vector k), cut-off plane z = 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.

4.20. and (M) = (2y - z) i + (x + y) j + xk, (p): x + 2y + 2z = 4

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

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