IDZ 10.2 - Option 10. 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)
1.10 S: y2 - z2 + x2 - 2xz + 2x = z, M0 (1, 1, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.10 z = ln (3x2 - 2y2)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.10 z = 6 (x - y) - 3x2 - 3y2

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.10 z = x2 + 2xy - 10, D: y = 0, y = x2 - 4