ответы ТР

№ задачи

1

2

3

4

5

1

0.139 (5/36)

0.167 (1/6)

0.0833 (1/12)

0.167 (1/6)

0.167 (1/6)

2

0.72

0.98

0.994

0.916

0.504

3

0.015

0.1035

0.628

0.085

0.86

4

0.914

0,8704 {0.953}

0.05792

2 {110})

45

5

M[X]

3

3.2

2.6

2.6

1.6

D[X]

2

1.56

2.24

2.24

10.24

6

C

0.667 (2/3)

12

1.5

0.25

5

M[X]

1.556

0.923 (12/13)

0

1.6

0.833 (5/6)

D[X]

0.0807

0.00507

0.6

0.107 (8/75)

0.0198 (5/252)

p

0.667 (5/12)

0.99976

0.0625

0.9375 (15/16)

1

F(x)

(x²-1)/3

x¹²

(x³+1)/2

x⁴/16

x⁵

7

g(y)

0.4,[0,1)

0.2,[1,4]

0.2,[0,2)

0.1,[2,8]

0.4,[1,3)

0.2,[3,4]

1,[2,3)

1/ (5y^1/2),[0,1)

1/ (10y^1/2),[1,16]

8

0

0.5

-0.5

0.296

-0.2964

C, Mx, My

0.5; 0.5; 1.0

0.5; 1.333; 0.6667

0.5; 2/3; 2/3(0.666)

1/6; 2.444; 0.8889

1/6;14/9(1.6); 16/18(0.9)

Dx,Dy,Kxy

0.03; 0.03; 0.0

0.222; 0.222; 0.111

2/9;2/9; -1/9(-0.11)

0.9136;0.321;0.161

0.914; 0.321; -0.16

№ задачи

6

7

8

9

10

1

0.5556 (5/9)

0.444 (4/9)

6.6-06

1.0-05

0.0156

2

0.846

0.9976

0.3024

0.8956 (0.8376)

0.8624

3

0.2105

0.3125

0.9075

0.6923

0.84

4

2.305-06

0.01132

0.678

0.9647

0.1159

5

M[X]

1.7

-2.3

0

2

1.8

D[X]

9.61

8.21

4.8

2

2.36

6

C

0.25

0.5

1

1.5

0.5

M[X]

0

1.57

0.785

0.5235

0

D[X]

1.333

0.4672

0.117 (1.85)

0.052 (0.274)

0.467

p

0.5

0.5

0.5

0.995 (0.5(1-cos3))

0.42 (0.5sin1)

F(x)

0.25x+0.5

(1-cosx)/2

(1-cos2x)/2

(1-cos3x)/2

(1+sinx)/2

7

g(y)

1/(9y^2/3), [-1,8]

2/ (9y^2/3), [0,1)

1/ (9y^2/3), [1,8]

1/ (6y^1/4), [0,1)

1/ (12y^1/4), [1,16]

1/(20y^4/5), [-32,32]

2/ (15y^4/5), [0,1)

1/ (15y^4/5), [1,32]

8

0.4472 (1/5^1/2)

-0.4472

-0.3636 (-4/11)

0.5

0.3636

C, Mx, My

1/8; 3.0; 1.0

1/8; 3; 1

1/6; 1.667; 0.833

½; 0.668;1.333;

1/6; 1.667; 1.1667

Dx,Dy,Kxy

1.667; 0.333;0.333

1.66675; 0.333; -0.33

1.22; 0.3056;-0.22

0.222; 0.222;0.111

1.222; 0.3056; 0.22

№ задачи

11

12

13

14

15

1

0.531 (9/10)⁶

5.0-06

0.6

0.4167 (5/12)

0.25

2

0.5964

0.8016

0.5076

0.9664

0.4116

3

0.788

0.667 (2/3)

0.3313

0.7

0.188

4

4 {0.25 }

1.91-04

0.3125

0.1094 (7/64)

5 (6)

5

M[X]

2

0

0.9

5

4.4

D[X]

1

2

2.69

1

2.64

6

C

2

1.0187

2

4

0.25

M[X]

0.285

0.925

0.5

0.25

0

D[X]

0.0354

0,883 (0.697)

0.25

1/16

2

p

0.159

0.237 (e-1)/e²

0.133

0.982 (e⁴-1)/e⁴

0.219

F(x)

Sin2x

1.0187(1-exp(-x))

1-exp(-2x)

1-exp(-4x)

(4 –x²)/8,[-2,0]

(4 +x²)/8,[0,2]

7

g(y)

0.05, [-8,12]

0.1, [0,6)

0.05, [6,14]

1/(4y²), [0.2,1]

1/(10y²), [1/11,1]

1/ (2.356(1-y²)^1/2

[0,0.707)

2/ (2.356(1-y²)^1/2

[0.707,1]

8

0

0

-0.189

0.189 (1/28^1/2)

0.866 (3^1/2/2)

C, Mx, My

¼;; 2; 2/3(0.6667)

1/8; 3; 5/6(0.833);

1/6; 2.667; 0.667

1/6; 3.33; 0.667

½; 2.0; 1.333

Dx,Dy,Kxy

0.667; 0.222; 0

1.667; 0.30556; 0

1.556; 0.222; -0.11

1.556; 0.222;0.111

0.667; 0.222;0.333

№ задачи

16

17

18

19

20

1

0.7

0.8

0.7

0.5

0.047

2

0.7416

0.9784

0.587

0.1512

0.9988

3

0.452

0.681

0.2813

0.036

0.191

4

15

0.685 (0.4977)

0.2765

0.0039 (1/256)

200

5

M[X]

-0.1

2.7

3.1

2.6

8

D[X]

21.29

20.21

19.49

9.14

2

6

C

0.582

6

0.0547 (7/128)

8

4.5

M[X]

0.582

0.857 (6/7)

1.75

0.889

0

D[X]

0.0793

0.0153

0.086

0.00988

0.818 (9/11)

p

0.378 (1/(e^1/2+1))

0.102

0.992 (127/128)

0.0039 (1/256)

0.5

F(x)

0.582 (exp(x)-1),

[0,1]

X⁶

X⁷/128

X⁸

(x⁹+1)/2

7

g(y)

2/ (3.1415(1-y²)^1/2),

[0,1]

2/ (3.1415(1-y²)^1/2),

[0,1]

2.67/ (3.14(1-y²)^1/2),

[0,0.707)

1.33/ (3.14(1-y²)^1/2),

[0.707,1]

1/y, [1,2.72]

0.667/y, [1,2.72)

0.333/y, [2.72,7.39]

8

-0.191

0

0.5

-0.5

0.191

C, Mx, My

1/10; 2.533; 0.933

1/8; 2.0; 1.0

1/4; 2.667; 0.667

¼; 1.333; 0.667

1/10; 3.47; 0.933

Dx,Dy,Kxy

2.249; 0.329; -0.164

1.333; 0.333; 0

0.889; 0.222; 0.222

0.889; 0.222; -0.22

2.249; 0.329;0.164

№ задачи

21

22

23

24

25

1

1/1785 (0.00056)

0.4084

0.695

0.25

0.333 (1/3)

2

0.889

0.6528

0.9188

0.7952

0.2982

3

0.511

0.2979

0.1858

0.4956

0.319

4

0.273

0.659

0.953

0.041

0.0039 (1/256)

5

M[X]

5.2

5.8

0

0

6.1

D[X]

9.96

8.56

46.4

63.2

4.59

6

C

10

5.5

0.721

2

2.667

M[X]

0.91 (10/11)

0

2.163

1.386

1.333

D[X]

0.00689

0.8462

0.728

0.0782

0.071

p

9.54-07

4.88-04

0.292

0.667 (2/3)

0.741

F(x)

X¹⁰

(x¹¹+1)/2

0.721lnx

2(1-1/x)

4/3(1-1/x²)

7

g(y)

1/ (2y^3/2), [0.25,1]

Y²/3, [-1,2]

0.667y² [0,1)

0.333y² [1,2]

1.2/ (3.14(1-y²)^1/2),

[0,0.5)

2.4/ (3.14(1-y²)^1/2),

[0.5,1]

0.75/ (3.14(1-y²)^1/2),

[-1,0.5)

1.5/ (3.14(1-y²)^1/2),

[0.5,1]

8

-0.3934

-0.223

0.5

0.263

0

C, Mx, My

1/8; 2.167; 8.333

1/9; 2.296; 0.926

¼; 1.33; 1.33

1/10; 2.6; 1.1

1/8; 4.0;0.667

Dx,Dy,Kxy

1.97; 0.3056;-0.306

1.91; 0.346;-0.182

0.889; 0.22;0.22

2.57; 0.32; 0.24

2.667;0.22; 0.0

№ задачи

26

27

28

29

30

1

0.1

0.3439 {0.0974}

0.001

0.05

0.6561

2

0.4032

0.5488

0.7648

0.4392

0.332

3

0.5

0.5

0.3036

0.667

0.4736

4

7.89-31 (1/2)¹⁰⁰

0.387 (0.3151)

0.659

0.4013

0,004096 (2/5)⁶

5

M[X]

3.3

5.9

3.05

4.25

8.55

D[X]

5.31

8.59

7.4475

6.488

4.548

6

C

3.12 (81/26)

64/15

5.2

128/21

896/127 (7.055)

M[X]

1.3846 (18/13)

56/45

1.2

1.181

1.157

D[X]

0.159 (27/13)

0.0624 (0.54)

0.042

0.646

0.0271

p

0.909

0.856

0.91 (0.8963)

1

0. (1)

F(x)

(27/26) (1-1/x³)

(16/15)(1-1/x⁴)

1.04(1-1/x⁵)

1.016(1-1/x⁶)

(128/127)(1-1/x⁷)

7

g(y)

2/ (3.14(1-y²)^1/2),

[0,1]

Y/2, [0,2]

0.8y, [0,1)

0.4y, [1,2]

Exp(y), [0,0.693]

0.47y³, [0,1)

0.235y³, [1,2]

8

0.159

-0.159

-0.0867

-0.064

-0.129

C, Mx, My

1/10; 4.4; 0.8

1/10; 3.6; 0.8

1/8; 3.08; 0.791

1/7.5; 2.9; 0.8

1/9; 3.33; 0.796

Dx,Dy,Kxy

2.91; 0.293; 0.147

2.91; 0.293; -0.146

1.99; 0.29; -0.066

1.648;0.304;-0.46

2.389; 0.29; -0.108