The document contains a C program that implements a bisection method to find the root of a specified function. It defines several functions including 'bisect' and 'myfunction', and the main function prompts the user for interval endpoints and error tolerance. The 'bisect' function operates iteratively to narrow down the search for the root, handling errors related to the possibility of no roots in the given interval.

1. #include
#include
double bisect(double x_left, double x_right, double epsilon,
double f(double argP), int *errP);
double myFunction(double rt);
void main()
{
double x_left, x_right, // interval endpoints
root, //Root that bisect will return
epsilon; //error tolerance
int err;
/*Ask user to enter endpoints and tolerance and store them*/
//Fill out here

2. //Utilize bisect function to search for root of myFunction
root=bisect(x_left, x_right, epsilon, myFunction, &err);
if (!err)
printf("n f(%.7f)= %en", root, myFunction(root));
return 0;
}
double bisect(double x_left, double x_right, double epsilon,
double f(double argP), int *errP){
double F_left, //value of myFunction at left endpoint
F_right, //value of myFunction at right endpoint
F_mid, //endpoint
x_mid; //interval mid point
int root_found=0; //This is a flag
/*???? Fill out here: Computes myFunction values at initial
endpoints of interval
and assign them to appropriate variables declared above*/

3. //If signs of value of each endpoint of myFunction are same
there may not be a unique root
//Hint: multiplication of numbers of same sign is always
larger than zero
if(/*??? Fill out here according to condition explained
above*/){
*errP=1;
printf("There may not be root in this interval: [%.6f,%.f]",
x_left, x_right);
exit(1); //Terminate the program if there may not be
any roots in this interval
}
else{
*errP=0;
//Search for root as long as interval length > epsilon and
no root found
while(/*???? Fill out here: enter the conditions for while
loop explained in previous line*/){
x_mid=//?? Computes mid point of the interval

4. F_mid=//??? Computes value of midPoint
if(F_mid==0.0){
root_found==1;
}
else if(/*Fill out here: enter the conditions for when
root is in [x_left, x_mid]*/){
//???? Update your x_right
}
else{
//???? Update your x_left
//???? Update your F_left
}
//Print root if found and interval, otherwise just new
interval
if(root_found)
printf("nRoot found at x x = %.6f, midpoint of
interval [%.6f, %.6f]", x_mid, x_left,x_right);

5. else
printf("nNew interval that root is searched: [%.6f,
%.6f]", x_left,x_right);
}//While-LOOP ends here
}
//If there is a root
return ((x_left+x_right)/2);
}
double myFunction(double x){
// Function that we look for its roots is 5x^5-2x^3+6x+3
int val;
/* ???? Fill out here: Compute the value of x for your
function (5x^5-2x^3+6x+3) and assign it to val */
return (val);

6. }