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Question 56: Write a C++ program to find a real root of the equation f(x) = 4x + sin x 5* = 0 in [0, 1] using the Regula- Falsi method. The two function values at the endpoints of the interval have opposite signs. Write user-defined C++ function to evaluate f(x) at any approximation. The iterations of the method should stop when either the approximation is accurate within 10-5, or the number of iterations exceeds 100, whichever happens first. #include #include using namespace std; #define TOL 0.000001 #define N 100 // error tolerance // maximum number of iterations // A user-defined C++ function double fval (double x) { double y = 4* x + sin(x) - exp(x); return y; } int main() { // Evaluating f(x) int k; double x0, x1, xn, xp , fxo, fxi , fxn , fxp, err; cout>a; cin>>b: // - Processing Section -// xn = b; x0 = a; xi = b; fx0 = fval(x0); fx1 = fval(x1); 1/ Calling/invoking fval with xD 1/ Calling/invoking fval with x0 for (k=2; k #include using namespace std; double fval(double x) double y = sqrt(x*x + 1); returnyi } int main() int n, double h , sum , 1, x0, xn, xc, fxo, fxn, fxc; // - Input Section // cout> x0; cout>n; cout>n; Processing Section --// // finding step size h = (xn- x0); fx=fval(x6); fron=fval(n); I = fx0+ fxn; xc = 0; sum = 0.0 for(j=1 ; j #include using namespace std; int main( { Int n.! doubleh, sumi, sumz,1,0,0, xc, x0, xn, foc; Input Section cout> XO: cout> cout>n; 11 Processing Section- -// // finding step size n - x - x0y; fxo - sqrt(xox0 - 1); xnsartxnx + 1) : I-DO+xn; XCXD : suml - 0.0; sum2 -0.0; for (1-1 ; j #include using namespace std; Int main() 1 Int n.! doubleh, sumi, sumz,1,0,0, xc, fx0, fx, fac; Input Section cout> x0; cout> xn; cout>n; 11- Processing Section // finding step size h = (xn - x0) : fx0 = sqrt(x0*x0 + 1); fxn = sqrt(xnxn + 1); I = fxo + fxn; xc = x0 ; sum1 = 0.0 ; sum 2 = 0.0 ; for(j=1 ; j