Алгоритм решения БДЗ / 04c

sin(ln x) = 0;

x 2 [22; 24]

xn+1 = xn

xn sin(log(xn))

cos(log(xn))

f′(x) =

cos(log(x))

6 0:0454 < 0; f′′(x) =

cos(log(x))

sin(log(x))

> 0:0018 > 0 ) x0 = 22

x

x2

x2

2

cos(ln x) = 0;

x 2 [110; 112]

xn+1 = xn +

xn cos(log(xn))

sin(log(xn))

f′(x) =

sin(log(x))

> 0:0089 > 0; f′′(x) =

sin(log(x))

cos(log(x))

6 0:00008165 < 0 ) x0 = 110

x

x2

x2

3

x cos x = 0;

x 2 [1; 2]

xn+1 = xn

xn cos(xn)

cos(xn)−xn sin(xn)

2:2347 < 0; f′′(x) =

2 sin(x)

x cos(x)

2:2990 < 0

x0 = 2

f′(x) = cos(x)

x sin(x)

6

6

)

4

sin x

= 0;

x 2 [3; 4]

x

xn+1 = xn

sin(xn)

xn

cos(xn)

−

sin(xn)

xn

xn2

)

cos(x)

sin(x)

2 sin(x)

sin(x)

2 cos(x)

(

f′(x) =

6 0:3457 < 0; f′′(x) =

> 0:1834 > 0 ) x0 = 3

x

x2

x3

x

x2

5

sin x

= 0; x

2 [2; 5; 3; 5]

x2

xn+1 = xn

sin(xn)

xn2

cos(xn)

2 sin(xn)

xn2

xn

3

)

cos(x)

2(sin(x) −

6 sin(x)

sin(x)

4 cos(x)

f′(x) =

6 0:2048 < 0; f′′(x) =

> 0:1020 > 0 ) x0 = 2:5

x2

x3

x4

x2

x3

6

sin x

ex

= 0;

x 2 [2; 5; 3]

10x

xn

sin(xn)−

e

x

= x

10

xn

cos(xn)−

exn

exn

n+1

n

+

10 xn

10 xn2

f′(x) = cos(x)

ex

+

ex

6 1:4363 < 0; f′′(x) =

ex

ex

sin(x)

ex

6 0:8519 < 0 ) x0 = 3

10 x

10 x2

5 x2

10 x

5 x3

7

arctan x + x 1 = 0;

x 2 [0; 1]

xn+1 = xn

xn

+arctan(x

)

−

1

n

1

+1

xn2+1

f′(x) =

1

+ 1

> 1:5000 > 0; f′′(x) =

2 x

0 ) x0 =?

x2+1

(x2+1)2

8

arctan x + x2 1 = 0;

x 2 [0; 1]

xn+1 = xn

arctan(xn)+1xn2−1

2 xn+

xn2+1

f′(x) = 2 x +

1

> 1:0000 > 0; f′′(x) = 2

2 x

> 1:3505 > 0 ) x0 = 1

x2+1

(x2+1)2

9

arccos(xn)+xn2− 23

arccos x + x2 3=2 = 0;

x 2 [0; 0; 1]

xn+1 = xn