Кузнецов_математика

D : x2 + y2 4 ≤1;

9.1.

= y2.

D: x29 + y2 25 ≤1;

9.3.y ≥ 0;

= x2 y.

D: 1≤ x29 + y2 4 ≤ 4;

9.5.y ≥ 0, y ≤ x2;= 8 yx3 .

D : x2 4 + y2 ≤1;

9.7.

= 4y4.

D : 1≤ x216 + y2 4 ≤ 4;

9.9.x ≥ 0, y ≤ x2;

= xy.

D : x24 + y2 ≤1;

9.11.x ≥ 0, y ≥ 0;= 6x3 y3.

D : x2 9 + y2 4 ≤1;

9.13.

= x2 y2.

D : x24 + y2 ≤1;

9.15.x ≥ 0, y ≥ 0;= 30x3 y7.

D: 1≤ x29 + y2 4 ≤ 2;

9.2.y ≥ 0, y ≤ 2 x;

3

= yx.

D: x29 + y2 25 ≤1;

9.4.y ≥ 0;

= 7x2 y18.

D : x29 + y2 ≤1;

9.6.x ≥ 0;

= 7xy6.

D: 1≤ x24 + y2 9 ≤ 4;

9.8.x ≥ 0, y ≤ 3x2;

= xy.

D : x24 + y2 9 ≤1;

9.10.x ≥ 0, y ≥ 0;

= x3 y.

D : 1≤ x24 + y2 ≤ 25;

9.12.x ≥ 0, y ≤ x2;

= xy3 .

D : x216 + y2 ≤1;

9.14.x ≥ 0, y ≥ 0;= 5xy7.

D : 1≤ x29 + y2 4 ≤ 3;

9.16.y ≥ 0, y ≤ 2 x;

3

= yx.

D: x2 + y2 25 ≤1;

9.17.y ≥ 0;

= 7x4 y.

D : x2 4 + y2 9 ≤1;

9.19.

= x2.

D : x29 + y2 ≤1;

9.21.x ≥ 0;

=11xy8.

D: 1≤ x29 + y2 4 ≤ 5;

9.23.x ≥ 0, y ≤ 2x3;

= xy.

D: x2 4 + y2 25 ≤1;

9.25.

= x4.

D : 1≤ x24 + y2 9 ≤ 36;

9.27.x ≥ 0, y ≥ 3 x;

2= 9xy3 .

D : x216 + y2 ≤1;

9.29.x ≥ 0, y ≥ 0;=105x3 y9.

D: 1≤ x216 + y2 ≤ 3;

9.31.x ≥ 0, y ≥ x4;

= xy5 .

D : x2 + y2 9 ≤1;

9.18.y ≥ 0;

= 35x4 y3.

D : 1≤ x2 + y2 16 ≤ 9;

9.20.y ≥ 0, y ≤ 4x;

= yx3 .

D: 1≤ x24 + y2 16 ≤ 5;

9.22.x ≥ 0, y ≤ 2x;

= xy.

D : x24 + y2 9 ≤1;

9.24.x ≥ 0, y ≥ 0;

= x5 y.

D : x2 + y2 4 ≤1;

9.26.x ≥ 0, y ≥ 0;=15x5 y3.

D : x2100 + y2 ≤1;

9.28.x ≥ 0, y ≥ 0;= 6xy9.

D : 1≤ x29 + y2 16 ≤ 2;

9.30.y ≥ 0, y ≤ 4 x;

3= 27yx5 .

618

10.13.

z = 0, z = 185 (3+ y ).

x2 + y2 = 8, x = 2y, x = 0, 10.15. z = 30y11, z = 0.

10.17.y = 63x, y = 3x, z = 0, x + z = 3.

10.2.

y = 5x, y = 5x3, z = 0, z = 5+ 5x3.

y= 5x3, y = 5x9,

10.10.z = 0, z = 5(3+ x )9. x + y = 4, y = 2x,

10.12.z = 3y, z = 0.

x =19 2y, x = 4 2y,

10.14. z = 0, z + y = 2.

x2 + y2 =18, y = 3x, y = 0,

10.19.z = 0, z = 5x11.

x = 7 3y, x = 2 3y,

10.21.z = 0, z + y = 3.

y= 15x, y = 15x,

10.25.z = 0, z = 15(1+ x ). x + y = 8, y = 4x,

10.27.z = 3y, z = 0.

x = y, x =15y,

10.29. z = 0, z =15(1+ y ).

x =17 2y, x = 2 2y,

10.31. z = 0, z + y =12.

x2 + y2 = 2y,

11.1. z = 54 − x2 , z = 0.

x2 + y2 = 82x,

11.3.z = x2 + y2 − 64, z = 0 (z ≥ 0).

11.4. z = 8 − y2 , z = 0.

x2 + y2 = 6x, x2 + y2 = 9x,

11.5.z = x2 + y2 , z = 0, y = 0 (y ≤ 0)

x2 + y2 = 2y,

11.7. z = 94 − x2 , z = 0.

x2 + y2 + 22y = 0,

11.9.z = x2 + y2 − 4, z = 0 (z ≥ 0).

x2 + y2 = 7x, x2 + y2 = 9x,

11.11.z = x2 + y2 , z = 0, y = 0 (y ≤ 0)

x2 + y2 = 2y,

11.13. z =134 − x2 , z = 0.

x2 + y2 = 62x,

11.15.z = x2 + y2 − 36, z = 0 (z ≥ 0).

x2 + y2 = 4x,

11.17. z =12 − y2 , z = 0.

x2 + y2 = 42x,

11.19.z = x2 + y2 −16, z = 0 (z ≥ 0).

x2 + y2 = 62y,

11.6.z = x2 + y2 − 36, z = 0 (z ≥ 0).

x2 + y2 = 2y, x2 + y2 = 5y,

11.8.

z = x2 + y2 , z = 0.

x2 + y2 = 4x,

11.10. z =10 − y2 , z = 0.

x2 + y2 = 82y,

11.12.z = x2 + y2 − 64, z = 0 (z ≥ 0).

x2 + y2 = 3y, x2 + y2 = 6y,

11.14.

z = x2 + y2 , z = 0.

x2 + y2 = 22y,

11.16.z = x2 + y2 − 4, z = 0 (z ≥ 0).

x2 + y2 = 8x, x2 + y2 =11x,

11.18.z = x2 + y2 , z = 0, y = 0 (y ≤ 0)

x2 + y2 = 4y,

11.20. z = 4 − x2 , z = 0.

x2 + y2 = 4y, x2 + y2 = 7y,

11.21.

z = x2 + y2 , z = 0.

x2 + y2 + 2x = 0,

11.23. z =174 − y2 , z = 0.

x2 + y2 + 22x = 0,

11.25.z = x2 + y2 − 4, z = 0 (z ≥ 0).

x2 + y2 =10x, x2 + y2 =13x,

11.27.z = x2 + y2 , z = 0, y = 0 (y ≥ 0)

x2 + y2 = 2x,

x2 + y2 = 42y,

11.22.z = x2 + y2 −16, z = 0 (z ≥ 0).

x2 + y2 = 9x, x2 + y2 =12x,

11.24.z = x2 + y2 , z = 0, y = 0 (y ≥ 0)

x2 + y2 = 4y,

11.26. z = 6 − x2 , z = 0.

x2 + y2 = 22x,

11.28.z = x2 + y2 − 4, z = 0 (z ≥ 0).

x2 + y2 = 5y, x2 + y2 = 8y,

11.30.

z = x2 + y2 , z = 0.

y = −6x2 + 8, y = 2,

12.5.z = x − x2 − y2 −1, z = x − x2 − y2 − 5.

x = 5y2 − 9, x = −4,

12.7.z = x2 + 4x − y2 − 4, z = x2 + 4x − y2 + 2.

x = 5y2 −1, x = −3y2 +1,

12.9.z = 2 − x2 + 6y2 , z = −1− x2 + 6y2 .

y = −5x2 + 3, y = −2,

12.11.z = 2x2 − 3y − 6y2 −1, z = 2x2 − 3y − 6y2 + 2.

x = 3y2 − 5, x = −2,

12.13.z = 2 − x2 +16y2 , z = 8 − x2 +16y2 .

y = 2x2 −1, y =1,

12.15.z = x2 − 5y2 − 3, z = x2 − 5y2 − 6.

x = −4y2 +1, x = −3,

12.17.z = x2 − 7y2 −1, z = x2 − 7y2 + 2.

y =1− 2x2 , y = −1,

12.19.z = x2 + 2y + y2 − 2, z = x2 + 2y + y2 +1.

y= 5x2 −1, y = −3x2 +1,

12.6.z = −2 + 3x2 + y2 , z = −5 + 3x2 + y2 .

y= 6x2 −1, y = 5,

12.8.z = 2x2 + x − y2 ,

z = 2x2 + x − y2 + 4.

x = −3y2 + 7, x = 4,

12.10.z = 2 + 6x2 + y2 , z = 3+ 6x2 + y2 .

y = x2 − 5, y = −x2 + 3,

12.12.z = 4 + 5x2 + 8y2 , z =1+ 5x2 + 8y2 .

x = y2 − 2, x = −4y2 + 3,

12.14.z = 16 − x2 − y2 + 2, z = 16 − x2 − y2 −1.

y = x2 − 2, y = −4x2 + 3,

12.16.z = 2 + x2 + y2 , z = −1+ x2 + y2 .

x = 7y2 − 6, x = −2y2 + 3,

12.18.z = 3−12y2 + 5x2 , z = −2 −12y2 + 5x2.

y = x2 − 7, y = −8x2 + 2,

12.20.z = 3−12y2 + 5x2 , z = −2 −12y2 + 5x2.

z= 16 − x2 − y2 ,

13.5. 9

2z = x2 + y2.

z = 21 x2 + y2 2,

13.9.

z = 232 − x2 − y2.

z = 1− x2 − y2 ,

13.13.

3z2 = x2 + y2.

z = 144 − x2 − y2 ,

13.17.

18z = x2 + y2.

z = 64 − x2 − y2 , z =1,

13.4. x2 + y2 = 60

(внутри цилиндра).

13.8. x2 + y2 = 51

(внутри цилиндра).

z = 16 − x2 − y2 ,

13.10.

6z = x2 + y2.

z = 81− x2 − y2 , z = 5,

13.12. x2 + y2 = 45

(внутри цилиндра).

z = 6 x2 + y2 ,

13.14.

z =16 − x2 − y2.

z = 64 − x2 − y2 , z = 4,

13.16. x2 + y2 = 39

(внутри цилиндра).

z = 3 x2 + y2 2,

13.18.

z = 52 − x2 − y2.

z = 49 − x2 − y2 , z = 3,

13.20. x2 + y2 = 33

(внутри цилиндра).

z = 36 − x2 − y2 ,

13.21.

9z = x2 + y2.

z = 4 9 − x2 − y2 ,

13.25.

z= x2 + y2.

z= 9 − x2 − y2 ,

z = 64 − x2 − y2 ,

13.29.

12z = x2 + y2.

z = 9 x2 + y2 ,

13.22.

z = 22 − x2 − y2.

z = 36 − x2 − y2 , z = 2,

13.24. x2 + y2 = 27

(внутри цилиндра).

z =12 x2 + y2 ,

13.26.

z = 28 − x2 − y2.

z = 25− x2 − y2 , z =1,

13.28. x2 + y2 = 21

(внутри цилиндра).

z = 9 x2 + y2 2,

13.30.

z =112 − x2 − y2.