IDZ 10.2 - Option 22. Decisions Ryabushko AP

IDZ 10.2 - Option 22. Decisions Ryabushko AP

1. Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)
1.22 S: x2 + 2y2 + z2 - 4xz = 8, M0 (0, 2, 0)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.22 z = arcsin (4x + y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.22 z = y√x - y2 - x + 6y

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.22 z = x3 + y3 - 3xy, D: x = 0, x = 2, y = -1, y = 2

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