1. Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)
1.20 S: x2 - y2 - z2 + xz + 4x = -5, M0 (-2, 1, 0)

2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.20 z = ln (4x2 - 5y3)

3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.20 z = 2xy - 3x2 - 2y2 + 10

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