IDZ 10.2 - Option 11. 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)

1.11 S: z = x2 + y2 - 2xy + 2x - y, M0 (-1, -1, -1)


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

2.11 z = e2x2 + y2


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

4. Examine the following function extremum.

4.11 z = x2 + xy + y2 - 6x - 9y


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

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