IDZ 10.2 - Option 24. 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)
1.24 S: x2 + y2 - 3z2 + xy = -2z, M0 (1, 0, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.24 z = sin√xy

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

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.24 z = x2 + 2xy - y2 - 4x, D: x = 3, y = 0, y = x + 1