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

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

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.2 z = x3 + 8y3 - 6xy + 5

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

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.