IDZ 10.2 - Option 1. Decisions Ryabushko AP

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• Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)

1.1 S: x2 + y2 + z2 + 6z - 4x + 8 = 0, M0 (2, 1, - 1)

• Find the second partial derivatives of the functions. Ensure that z "xy = z" yx

2.1 z = ex2-y2

• To verify whether the above equation the function u.

• Examine the following function extremum.

4.1 z = y√x - 2y2 - x + 14y

• Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.

5.1 z = 3x + y - xy, D: y = x, y = 4, x = 0

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