IDZ 10.2 - Option 8. 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)
1.8 S: x2 + y2 - xz - yz = 0, M0 (0, 2, 2)

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

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.8 z = x2 + xy + y2 + x - y + 1

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.8 z = 3x + 6y - x2 - xy - y2, D: x = 0, x = 1, y = 0, y = 1