Taylor’s Series
#include<stdio.h>
#include<conio.h>
#define Y1 x*x+y*y
#define Y2 2*x+2*y*(x*x+y*y)
#define Y3 2+2*(x*x+y*y)*(x*x+y*y)+2*y*(2*x+2*y*(x*x+y*y))
#define Y4 6*(x*x+y*y)*(2*x+2*y*(x*x+y*y))+2*y*(2+2*(x*x+y*y)*(x*x+y*y)+2*y*(2*x+2*y*(x*x+y*y)))
int main (void)
{
float h,a,b,c=0,n,i,ya,yb,yc,yd,x,y;
clrscr();
printf("Enter the valu of a & b as Y(a)=b: ");
scanf("%f%f",&a,&b);
printf("Enter the value of h: ");
scanf("%f",&h);
printf("Enter the value of x: ");
scanf("%f",&n);
x=a;
y=b;
for(i=a;i<n;i=i+h)
{
ya=Y1; printf("\n\t%f",ya);
yb=Y2; printf("\n\t%f\t%f\t%f\t%f",Y1,y,x,yb);
yc=Y3; printf("\n\t%f\t%f\t%f\t%f",Y2,y,x,yc);
yd=Y4; printf("\n\t%f",yd);
y=y+ya*h+(yb*h*h)/2+(yc*h*h*h)/6+(yd*h*h*h*h)/24;
x=x+h;
c++;
printf("\n\t\t%f",y);
}
printf("\nItaration no. %f\nRequired ans: %f",c,y);
getch();
return 0;
}