Please write in Language c using only the files stdio.h and math.h
Suppose you wish to find the root r of a function f(x), that is, the value r where f(r)=0. One method is to make an initial guess, x0, compute the line tangent to f at x0, and find where the tangent line intercepts the x-axis, x1. Then, use x1 as the second guess and repeat this procedure n times until f(xn) approximately equals 0 and report xn as the root r. In the figure we see successive tangent lines of the function f(x) in red eventually intercept the xaxis at the root r.
The Taylor series of a function f(x) that is infinitely
differentiable at a number x0, is approximately
Setting this equation to 0, we have
Write a program using an iteration structure to calculate the approximate root of the equation
Prompt the user to enter an initial guess x0. Example output:
Hi, According to your question, you need a C program that uses only 2 header files, i.e., 'main.h' and 'math.h' for finding the roots of the equation .
The given equation can be re-written as .
The differentiation of given eqn is .
The program for the same is given below:
*************************MAIN.C************************
#include<stdio.h>
#include<math.h>
long double f(long double x) //The given function f(x)
{
return x*x*x-2*x*x+x-3;
}
long double df (long double x) // Differentiation of given function
df(x)
{
return 3*x*x-4*x+1;
}
int main() // The main function
{
int itr, maxmitr=20; // Variables for iteration and maximum allowed
iterations
long double h, x0, x1, allerr=0.1e-50; // Variables for allowed
errors, initial value of x as x0, next value of x as x1, h as the
difference and allerr as allowed error
printf("?");
scanf("%Lf", &x0);
printf("i\t\t\t\t\t\t\t\tx\t\t\t\tf(x)\n"); // For formatting
stuffs
printf("%02d\t%.30Lf\t%Le\n", 0, x0, f(x0));
for (itr=1; itr<=maxmitr; itr++)
{
h=f(x0)/df(x0);
x1=x0-h;
printf("%02d\t%.30Lf\t%Le\n", itr, x1, f(x1));
if (fabsl(h) < allerr)
{
printf("%02d\t%.30Lf\t%Le\n", itr, x1, f(x1));
return 0;
}
x0=x1;
}
printf("Solution does not converge or iterations are
insufficient\n");
return 1;
}
*************************MAIN.C ENDs*******************
The images of the above program are:
The output of the above program are:
Run1:
Run2:
Run3:
I hope this will help you. I have added comments in assistance with
the code to be understandable. If you have any query related to the
above question feel free to ask.
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