IDZ 10.2 - Option 3. 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)
1.3 S: x2 + y2 + z2 - xy + 3z = 7, M0 (1, 2, 1)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.3 z = tg (x / y)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.3 z = 1 + 15x - 2x2 - xy - 2y2

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.3 z = x2 + 2xy - 4x + 8y, D: x = 0, x = 1, y = 0, y = 2