IDZ 10.2 - Option 19. 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)

1.19 S: x2 + y2 - z2 + xz + 4y = 4, M0 (1, 1, 2)


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

2.19 z = arctg (2x - y)


3. To verify whether the above equation the function u.

4. Examine the following function extremum.

4.19 z = xy - x2 - y2 + 9


5. Find the maximum and minimum values \u200b\u200bof the function z = z (x, y) in D, given the limited lines.

5.19 z = xy - 3x - 2y, D: x = 0, x = 4, y = 0, y = 4