IDZ 10.2 - Option 12. Decisions Ryabushko AP
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1. Find the equation of the tangent plane and the normal to the given surface S at the point M0 (x0, y0, z0)
1.12 S: z = y2 - x2 + 2xy - 3y, M0 (1, -1, 1)
2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.12 z = ctg (y / x)
3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.12 z = (x - 2) 2 + 2y2 - 10
5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.12 z = 1 / 2x2 - xy, D: y = 8, y = 2x2
1.12 S: z = y2 - x2 + 2xy - 3y, M0 (1, -1, 1)
2. Find the second partial derivatives of the functions. Ensure that z "xy = z" yx
2.12 z = ctg (y / x)
3. To verify whether the above equation the function u.
4. Examine the following function extremum.
4.12 z = (x - 2) 2 + 2y2 - 10
5. Find the maximum and minimum values of the function z = z (x, y) in D, given the limited lines.
5.12 z = 1 / 2x2 - xy, D: y = 8, y = 2x2
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