22

17.10

= 8xi - 2 y

,

s : {x + y = 1, z = x 2 + y 2 , x = 0, y = 0, z = 0}.

a

j

+ xk

17.11

= 2xi -y

+ z

,

s : {9 - z = x 2 + y 2 ,0 £ z £ 9)}.

a

k

j

17.12

=

yi + 5 y

+ z

,

s : {x 2

+ y 2

= 1, z = x, z = 0, (z ³ 0)}.

a

j

k

17.13

=

yi + (x + 2 y)

,

s : {x 2

+ y 2

= 2x, z = x 2

+ y 2 , z = 0}.

a

j

+ xk

17.14

=

xi - 2 y

,

s : {z = x 2 + y 2 , z = 2x}.

a

j

+ 3zk

17.15

= - 2xi + z

+ (x + y)

,

s : {x 2

+ y 2

= 2 y, z = x 2

+ y 2 , z = 0}.

a

j

k

17.16

=

x 2 i + x

+ xz

,

s : {z = x 2 + y 2 , z = 1, x ³ 0, y ³ 0}.

a

j

k

17.17

=

x 2 i + y

+ z

,

s : {x 2

+ y 2

+ z 2

= 1, z = 0, (z ³ 0)}.

a

j

k

17.18

= xzi + z

,

s : {1 - z = x 2 + y 2 , z = 0)}.

a

j

+ yk

17.19

= 3x2 i - 2x 2 y

+ (2x -1)z

,

s : {x 2

+ y 2

= 1, z = 0, z = 1}.

a

j

k

17.20

=

yi + y 2

+ yz

,

s : {z = x 2 + y 2 , z = 1, x ³ 0, y ³ 0}.

a

j

k

17.21

=

y 2 xi + x 2 y

+

z 3

,

s : {x 2

+ y 2

+ z 2

= 1, z = 0, (z ³ 0)}.

a

j

k

3

s : {z = 2 - 4(x 2

+ y 2 ), z = 4(x 2 + y 2 )}.

17.22

a

= (2x + y)i + ( y + 2z)

k

,

17.23

=

x 2 i + y 2

+ z 2

,

s : {x 2

+ y 2

+ z 2

= 1, x ³ 0, y ³ 0, z ³ 0}.

a

j

k

17.24

= x 2 i + xy

,

s : {x 2 + y 2 = z 2 , z = 4}.

a

j

+ 3zk

ì

2

2

2

2

1

ü

17.25

a = (2 y -15x)i + (z - y) j - (x - 3y)k ,

s : íz

= 3x

+ 3y

+1, x

+ y

=

, z

=

0ý .

4

î

þ

9

28

65

126

18.3

1

+

1

+

1

+

1

+K

3

8

15

24

18.4

1

+

1

+

1

+

1

+K

1× 4 4 ×7 7 ×10 10 ×13

18.5

1 +

3

+

1

+

3

+

1

+K

1× 2 1× 2 ×3 1× 2 ×3 × 4 1× 2 ×3 × 4 ×5

18.6

1

+

4

+

9

+K

1× 2 ×3 1× 2 ×3 × 4 ×5 1× 2 ×3 × 4 ×5 × 6 × 7

18.7

1

+

3

+

5

+K

1× 4

4 ×9

9 ×16

18.8

1 +

1 +1

+

4 +1

+

9 +1

+K

2 ×1 4 ×1× 2 8 ×1× 2 ×3

23

18.12

1 +

1× 2 ×3

+

1× 2 ×3 × 4 ×5

+

1× 2 ×3 × 4 ×5 × 6 ×7

+K

1× 2

1× 2 ×3

1× 2 ×3 × 4

18.13

1

+

1× 4

+

1× 4 × 7

+

1× 4 × 7 ×10

+K

2 2 ×7 2 × 7 ×12 2 × 7 ×12 ×17

18.14

3 +

5

+

9

+

17

+

33

+K

8

27

64

125

6

8

Cos

2

p

Cos

4

p

Cos

p

Cos

p

3

18.15

3

+

3

+

3

+

+L

2

5

10

17

18.16

ln2

+

ln3

+

ln4

+

ln5

+L

2

5

10

17

18.17

2

+

4

+

5

+

6

+K

3

24

29

216

18.18

1×32

+

2 ×34

+

3 ×36

+K

2

4

8

1

1

1

1

18.20

1×3

+

2 × 4

+

3 ×5

+

4 ×6

+K

1× 2 1× 2 ×3 1× 2 ×3 × 4 1× 2 ×3 × 4 ×5

18.21

2

+

4

+

6

+

8

+K

3 ×3

7 ×9

11× 27

15 ×81

18.22

4

+

7

+

10

+K

1× 1× 2 4 ×

2 ×3 27 ×

3 × 4

1×8 1×8 ×27 1×8×27 ×64

18.24

1

+

1×3

+

1×3 ×5

+

1×3 ×5 × 7

+K

2 2 ×5 2 ×5 ×8 2 ×5 ×8 ×11

18.25

1 +

24

+

124

+

624

+K

7

10

13

¥

1

¥

2

19.1

å

19.2 å

n-1

+ n -1

n=1 3 n 2 (n2 + 4)

n=1 5

¥

1

¥

1

19.3

å

19.4 å

(n +1)3 n + 5

n(n -1)

n=1

n=1

¥

ln n

¥

1

19.5

å

19.6 å

n

3

n(n +1)(n + 2)

n=1

+ n +1

n=1

¥

n

¥

1

19.7

å

19.8 å

n

4

n - ln n

n=1

+ 9

n=1