The Complete Codes

C program to find value using Bisection Method | C Programming #include<stdio.h> #include<conio.h> #include<math.h> #define EST 0.05 #define F(x) pow(x,3)-x-3 int main() { int i=1; float xl,xu,xm,f1,f2,f3,error; printf("Enter the values for xl and xu respectively\n"); scanf("%f%f",&xl,&xu); printf("Iteration\tXl\t Xu\t f(Xm)\t Error\n"); do { xm=(xl+xu)/2; f1=F(xl); f2=F(xu); f3=F(xm); error=fabs((xl-xu)/xu); if((f1*f3)<0) { xu=xm; } else { xl=xm; } f3=F(xm); error=fabs((xl-xu)/xu); printf("%d\t %.4f\t %.4f\t%.4f\t %.4f\n",i,xl,xu,xm,error); i++; }while (error>=EST); }

C program to find value using secant method | C programming #include<stdio.h> #include <math.h> #include<conio.h> #define EST 0.05 #define F(x) x-exp(x)+2 int main() { int i = 1; float x0,x1,a,b,c,d,f1,x2,f0,error; printf("\nEnter the value of x0: "); scanf("%f",&x0); printf("\nEnter the value of x1: "); scanf("%f",&x1); printf("\n__________________________________________________________________\n"); printf("\niteration\tx0\t x1\t f0\t f1\t x2\t\terror"); printf("\n___________________________________________________________________\n"); f0=F(x0); f1=F(x1); x2=x1-((f1*(x1-x0))/(f1-f0)); printf("%f",x2); error=fabs((x2-x1)/x2); printf("\n %d \t %.2f\t %.2f\t %.2f \t %.3f \t %.3f \t %.3f", i, x0,x1,f0,f1,x2,error); do{ i++; x0=x1; f0= f1; x1=x2; f0=F(x0); f1=F(x1); x2=x1-((f1*(x1-x0))/(f1-f0)); error=fabs((x2-x1)/x2); printf("\n %d \t %.2f\t %.2f\t %.2f \t %.4f \

C program to find the value using Newton Raphson Before starting with the program let us learn something about Newton Raphson Method Newton Raphson Method  is open method and starts with one initial guess for finding real root of non-linear equations. In other Words,  Newton Raphson method, also called the Newton’s method, is the fastest and simplest approach of all methods to find the real root of a nonlinear function. It is an open bracket approach, requiring only one initial guess. This method is quite often used to improve the results obtained from other iterative approaches

C program to calculate the Chinese remainder theorem  #include <stdio.h> int main () {     int user_num [ 2 ];     int numbers [ 4 ];     int a [ 10 ][ 10 ];     int i , j , sum [ 4 ];     printf ( " \n Enter two numbers of seven digits: \n " );     for ( i = 0 ; i <= 1 ; i ++)     {         scanf ( " %d " , & user_num [ i ]);     }     printf ( " \n\n Enter four relative prime numbers: \n " );     for ( i = 0 ; i < 4 ; i ++)     {         scanf ( " %d " , & numbers [ i ]);     }     for ( i = 0 ; i < 2 ; i ++)     {         for ( j = 0 ; j < 4 ; j ++)         {             a [ i ][ j ] = user_num [ i ] % numbers [ j ];         }     }     for ( i = 0 ; i < 4 ; i ++)     {         j = 0 ;         sum [ i ] = ( a [ j ][ i ] + a [ j + 1 ][ i ]) % numbers [ i ];     }     printf ( " \n\n The tuple of 4 numbers is: \n\n " );     printf ( "(" );     for ( i = 0 ; i < 4

C Program To Generate Permutation #include <stdio.h> long int fact ( int x ) {     long int f = 1 ;     int i ;     for ( i = 1 ; i <= x ; i ++)         f = f * i ;     return ( f ); } int main () {     int n , r , i , p ;     printf ( "Enter value of n and r : " );     scanf ( " %d %d " , & n , & r );     if ( n >= r )     {         p = fact ( n ) / fact ( n - r );         printf ( "Permutation P( %d , %d ) = %d " , n , r , p );     }     else     {         printf ( "Wrong Input ! Enter n>=1 ." );     }     return 0 ; } C Programming To Generate Combination | C Programming #include <stdio.h> long int fact ( int x ) {     long int f = 1 ;     int i ;     for ( i = 1 ; i <= x ; i ++)         f = f * i ;     return ( f ); } int main () {     int n , r , i , ncr ;     printf ( "Enter value of n and r : " );     scanf ( " %d %d " , & n , & r );

Implication:- The statement “p implies q” means that if p is true, then q must also be true. The statement “p implies q” is also written “if p then q” or sometimes “q if p.” Statement p is called the premise of the implication and q is called the conclusion.

C++ Program for modular search and linear search using recursion function Before starting with the program to find binary search and linear search using recursion function let us know about recursion function and Modular Search. Recursion Function Recursion is a process by which a function call itself repeatedly until some specified condition has been satisfied.                  The process is used for repetitive computation in which action is stated in terms of previous result.                  In order to solve a problem recursively two condition must be satisfied. The problem must be written in a recursive form. The problem statement must include a problem stopping condition.