1. Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)
1.14 S: x2 - 2y2 + z2 + xz - 4y = 13, M0 (3, 1, 2)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.14 z = cos (x2y2 - 5)

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

5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.14 z = 2x2 + 3y2 + 1, D: y = √9-9 / 4x2, 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.