Plz solve the question using c programming without using the library # include stdlib.h. or string.h ..Only use # include stdio.h and # include math.hAnd printf, scanf, fout, fin. 4. In your Calculus course you will learn that the function ln(1 + x) can be approximated by apolynomial of degree n as follows:1≈x-x+2Here is a sample run:x = 0.900000n=52133approximate value = 0.692073actual value = 0.641854relative error = 7.824064 percent1pea4In(1+x)=x-This is called a power series approximation.Write a program to check the accuracy of this formula. Your program must prompt the userfor the value of x (where [x] < 1) and the degree, n, of the polynomial to use. Your programshould then write the values of x, n, the approximation, the actual value and the percentrelative error to the output file powerseriesout.txt.++For marking purposes use x = 0.9 and n = 40.... + (−1)(¹+¹)x” /n

Answered: polynomial of degree n as follows: 1…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Plz solve the question using c programming without using the library # include stdlib.h. or string.h .. Only use # include stdio.h and # include math.h And printf, scanf, fout, fin.

4. In your Calculus course you will learn that the function ln(1 + x) can be approximated by a
polynomial of degree n as follows:
1
≈x-x+
2
Here is a sample run:
x = 0.900000
n=5
2
1
3
3
approximate value = 0.692073
actual value = 0.641854
relative error = 7.824064 percent
1
pea
4
In(1+x)=x-
This is called a power series approximation.
Write a program to check the accuracy of this formula. Your program must prompt the user
for the value of x (where [x] < 1) and the degree, n, of the polynomial to use. Your program
should then write the values of x, n, the approximation, the actual value and the percent
relative error to the output file powerseriesout.txt.
+
+
For marking purposes use x = 0.9 and n = 40.
... + (−1)(¹+¹)x” /n

Expert Solution

Step 1

include <stdio.h>
#include <stdlib.h>
#include<math.h>

int main()
{
float x,sum=0,dev;
int n,i;
FILE *fp=fopen("powerseriesout.txt","w");
printf("Enter Value for x");
scanf("%f",&x);
printf("Enter The Degree for x");
scanf("%d",&n);
for(i=1;i<n+1;i++)
{
sum+=((pow(-1,i+1)*pow(x,i))/i);
}
fprintf(fp,"x =%f\n",x);
fprintf(fp,"n =%d\n",n);
fprintf(fp,"Approximate Value =%f\n",sum);
fprintf(fp,"Actual Value =%f\n",log(1+x));
dev=sum-log(1+x);
dev/=log(1+x);
dev*=100;
fprintf(fp,"Relative Error =%f percent",dev);
}

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