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. [a, b] (.4.4).

.4.4. .

f(a) f(b). f(a)*f(b)>0, . f(a)*f(b)<0, .. [a, b] f(x) , . . a y1 = f(a). x b, y2 = f(x). , f(a)*f(x)>0, [x, b], [a, x]. , , , = b = x. , [a, b], . , [a, b] . x = (a+b)/2.

 

4.4. e = 0.01 , [1,3].

#include <iostream>

#include <conio.h>

#include <math.h>

#include <stdlib.h>

using namespace std;

 

int main()

{ int n = 0;

float x, a = 1, b = 3, y1, y2, eps = 0.001, e, r, l;

l = a; r = b;

y1 = a*a*a 2*a*a 3;

y2 = b*b*b 2*b*b 3;

if (y1*y2>0) { cout << " " <<endl;

getch();

exit(1);

}

do { ++n;

x = (a+b)/2;

y1 = a*a*a 2*a*a 3;

y2 = x*x*x 2*x*x 3;

if (y1*y2>0) a = x;

else b = x;

} while ((b a)>eps);

x = (a + b)/2;

cout << " "<< l << ", " << r << " " << x << " " << n <<"";

cout << endl;

return 0; }

1

Eps.

1, 16
2, 17
3, 18
4, 19
5, 20
6, 21
7, 22
8, 23
9, 24
10, 25
11, 26
12, 27
13, 28
14, 29
15, 30

 

 

2

1, 16 x + ln(x + 0.5) 0.5 = 0 [0, 2]. . .
2, 17 2x3 + 4x 1 = 0 [0, 0.5]. . .
3, 18 1/x = sin x [0.1, 2]. . .
4, 19 . 0.001. .
5, 20 x4 + 2x3 x 1 = 0 [0, 1]. 0.00015. .
6, 21 x3 + 12x 2 = 0 [0.1, 1]. 0.00015. .
7, 22 . 0.001. .
8, 23 x5 x 0.2 = 0 [0.9,1.1]. 0.0001. .
9, 24 5x + 8lnx 1 = 0 [0.5, 1]. 0.0015. .
10, 25 0.001. .
11, 26 x3 2x2 + x 3 = 0 [2.1, 2.2]. 0.001. .
12, 27 x3 + x2 3 = 0 [0.5, 3]. 0.00001. .
13, 28 . 0.001. .
14, 29 . 0.001. .
15, 30 . 0.001. .




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