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Muhammad Al-Xorazmiy nomida Toshkent Axborot texnologiyalari universiteti
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| Sana | 21.05.2024 | | Hajmi | 1,07 Mb. | | #247879 |
Bog'liq al by farrukh
Muhammad Al-Xorazmiy nomida Toshkent Axborot texnologiyalari universiteti
2 - amaliy ish
Bajardi: Zokirov Farruxbek
amaliy
24-variant
1-topshiriq
Tenglamaning ildizlarini grafik usulda ajrating va uning taqribiy yechimlarini e=0.001 aniqlikda yuqorida sanab o‘tilgan barcha usullar yordamida toping va natijalarni tahlil qiling.
a)
1.oraliqni teng ikkita bo‘lish usuli
#include
#include
double f(double x) {
return pow(x, 3) - 4*x + 1;
}
int main() {
double a = 0.1; // boshlang'ich taxmin
double b = 2.0; // oxirgi taxmin
double epsilon = 1e-6; // aniqlik
while (b - a > epsilon) {
double c = (a + b) / 2.0;
if (f(c) == 0.0) {
break;
} else if (f(a) * f(c) < 0.0) {
b = c;
} else {
a = c;
}
}
double x = (a + b) / 2.0;
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
2.oddiy ketma-ketlik usuli
#include
#include
double f(double x) {
return pow(x, 3) - 4*x + 1;
}
int main() {
double x = 0.1; // boshlang'ich taxmin
double epsilon = 1e-6; // aniqlik
double dx = 0.01; // qadam o'lchami
while (abs(f(x)) > epsilon) {
x = x + dx;
}
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
3. urinmalar usuli
#include
#include
double f(double x) {
return pow(x, 3) - 4*x + 1;
}
double df(double x) {
return 3*pow(x, 2) - 4;
}
int main() {
double x = 1.0; // boshlang'ich taxmin
double epsilon = 1e-6; // aniqlik
while (abs(f(x)) > epsilon) {
x = x - f(x) / df(x);
}
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
b)
1. oraliqni teng ikkita bo‘lish usuli
#include
#include
double f(double x) {
return log(x) * sqrt(x);
}
int main() {
double a = 0.1; // boshlang'ich taxmin
double b = 2.0; // oxirgi taxmin
double epsilon = 1e-6; // aniqlik
while (b - a > epsilon) {
double c = (a + b) / 2.0;
if (f(c) == 0.0) {
break;
} else if (f(a) * f(c) < 0.0) {
b = c;
} else {
a = c;
}
}
double x = (a + b) / 2.0;
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
2. oddiy ketma-ketlik usuli
#include
#include
double f(double x) {
return log(x) * sqrt(x);
}
int main() {
double x = 0.1; // boshlang'ich taxmin
double epsilon = 1e-6; // aniqlik
double dx = 0.01; // qadam o'lchami
while (abs(f(x)) > epsilon) {
x = x + dx;
}
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
urinmalar usuli
#include
#include
double f(double x) {
return log(x) * sqrt(x);
}
double df(double x) {
return 1/x - 1/(2*sqrt(x));
}
int main() {
double x = 1.0; // boshlang'ich taxmin
double epsilon = 1e-6; // aniqlik
while (abs(f(x)) > epsilon) {
x = x - f(x) / df(x);
}
std::cout << "Tenglama ildizi " << x << " ga teng" << std::endl;
return 0;
}
Topshiriq
1.To’g’ri To’rtburchaklar usuli
#include
#include
double f(double x) {
return cos(x) / sqrt(4*pow(x,3) - x);
}
double rectangle_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = 0;
for(int i = 0; i < n; i++) {
sum += f(a + i * h);
}
return sum * h;
}
int main() {
double a = 0.8;
double b = 1.6;
int n = 1000; // interval soni
std::cout << "Integral: " << rectangle_method(a, b, n) << std::endl;
return 0;
}
2.Trapetsiyalar usuli
#include
#include
double f(double x) {
return cos(x) / sqrt(4*pow(x,3) - x);
}
double trapezoidal_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = 0.5 * (f(a) + f(b));
for(int i = 1; i < n; i++) {
sum += f(a + i * h);
}
return sum * h;
}
int main() {
double a = 0.8;
double b = 1.6;
int n = 1000; // interval soni
std::cout << "Integral: " << trapezoidal_method(a, b, n) << std::endl;
return 0;
}
3.Simpsonlar (parabolalar) usuli
#include
#include
double f(double x) {
return cos(x) / sqrt(4*pow(x,3) - x);
}
double simpsons_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = f(a) + f(b);
for(int i = 1; i < n; i++) {
if (i % 2 == 0) {
sum += 2 * f(a + i * h);
} else {
sum += 4 * f(a + i * h);
}
}
return sum * h / 3;
}
int main() {
double a = 0.8;
double b = 1.6;
int n = 1000; // interval soni
std::cout << "Integral: " << simpsons_method(a, b, n) << std::endl;
return 0;
}
1.To’g’ri To’rtburchaklar usuli
#include
#include
double f(double x) {
return sin(x + 2) * x / (3 * x);
}
double rectangle_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = 0;
for(int i = 0; i < n; i++) {
sum += f(a + i * h);
}
return sum * h;
}
int main() {
double a = 12;
double b = 2;
int n = 1000; // interval soni
std::cout << "Integral: " << rectangle_method(a, b, n) << std::endl;
return 0;
}
Trapetsiyalar usuli
#include
#include
double f(double x) {
return sin(x + 2) * x / (3 * x);
}
double trapezoidal_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = 0.5 * (f(a) + f(b));
for(int i = 1; i < n; i++) {
sum += f(a + i * h);
}
return sum * h;
}
int main() {
double a = 12;
double b = 2;
int n = 1000; // interval soni
std::cout << "Integral: " << trapezoidal_method(a, b, n) << std::endl;
return 0;
}
Simpsonlar (parabolalar) usuli
#include
#include
double f(double x) {
return sin(x + 2) * x / (3 * x);
}
double simpsons_method(double a, double b, int n) {
double h = (b - a) / n;
double sum = f(a) + f(b);
for(int i = 1; i <= n - 1; i++) {
if (i % 2 == 0) {
sum += 2 * f(a + i * h);
} else {
sum += 4 * f(a + i * h);
}
}
return sum * h / 3;
}
int main() {
double a = 12;
double b = 2;
int n = 1000; // interval soni
std::cout << "Integral: " << simpsons_method(a, b, n) << std::endl;
return 0;
}
3-Topshiriq
N=24
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