Алгоритм решения БДЗ / 05c

1

sin(arctan x)

x0 = 0; x1 = =2; x2 =

P2 =

0:1488x2 + 0:7707x; f′′′(x) =

18 x2

3

15 x4

(x2+1)

5

3

(x2

7

′′′

2

(x2+1) 2

+1) 2

jR2(x)j =

|f

3!( )|

j!3(x)j

6 63 1:4917 0:7459

2

3e2x

x0 = 7; x1 = 8; x2 = 9

x

P2 = 0:0787 108x2 1:1521 108x + 4:2145 108; f′′′(x) =

24 e2 x

36 e2 x

+

36 e2 x

18 e2 x

x

x2

x3

x4

|f ′′′( )|

6

1:4897

108

6

jR2(x)j =

j!3(x)j

6 ·

0:3849

9:5563 10

3!

3

cos(arcsin x + )

x0 = 1=2; x1 = 0; x2 = 1=2

P2 = 0:5359x2

1:0000; f′′′(x) =

3 x3

3 x

+

5

3

′′′

(1−x2) 2

(1−x2) 2

jR2(x)j =

|f

3!( )|

j!3(x)j

6 3:07926

0:0481 0:0247

4

(sin x)2 + 2x

x0 = 1=2; x1 = 0; x2 = 1=2

P2 = 0:9194x2 + 2:0000x; f′′′(x) = 8 cos(x) sin(x)

′′′

jR2(x)j =

|f

3!( )|

j!3(x)j

6 3:36596

0:0481 0:0270

5

7 ln x x

x0 = 1=2; x1 = 1; x2 = 2

P2 = 3:2347x2 + 13:5561x 11:3214; f′′′(x) = x143

′′′

jR2(x)j =

|f

3!( )|

j!3(x)j

6 1126

0:2641 4:9293

6

cos(sin(x= )) x0 = 4; x1 = 5; x2 = 6

( (

))

(

)

( (

)) (

)

3

( (

)) (

) (

)

P2 = 0:0415x2

0:4102x + 1:5527; f′′′(x) =

sin sin

x

cos

x

+

sin sin

x

cos

x

+

3 cos sin

x

cos

x

sin

x

3

3

3

′′′

jR2(x)j =

|f

3!( )|

j!3(x)j

6 0:02756

0:3849 0:0018

7

1=x + cos x

x0 = 2; x1 = 3; x2 = 4

P2 = 0:4968x2 3:2243x + 4:5455; f′′′(x) = sin(x)

6

x4

′′′

jR2(x)j =

|f

3!( )|

j!3(x)j

6 0:78026

0:3849 0:0501

8

p

ln(3x) x

x0 = 3; x1 = 4; x2 = 5

P2 =

0:0163x2 + 0:1340x + 0:2100; f′′′(x) =

2

3

3

8 x

5

′′′

x

2

jR2(x)j =

|f

3!( )|

j!3(x)j

6 0:05006

0:3849 0:0032

9

1

x0 = 1; x1 = 0; x2 = 1

1 + x2

P2 = 0:5000x2 + 1:0000; f′′′(x) =

24 x

48 x3

(x2+1)3

(x2+1)4

′′′

jR2(x)j =

|f

3!( )|

j!3(x)j

6 4:66756

0:3849 0:2994