Question

Must be written in basic C language. I keep getting stuck with my code.

Step 1: You are to write an algorithm to compute e1 using the Taylor Series Expansion n! o Use the highest precision possible Step 2: Calculate the error between your algorithm and the value computed using the function exp(x) found in the <math.h> library. .Step 3: Calculate how many digits of precision is your algorithm.

Answer 1

Here is the code for you:

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

long int fact(int n)
{
    if(n == 0)
        return 1;
    return n * fact(n-1);  
}
long double expCalc(int x)
{
    long double sum = 0, previousSum = 0;
    int i = 0;
    while(1)
    {
       sum += pow(x, i) /fact(i);
       if(sum < 0)
           return previousSum;
       //printf("%Lf\t%Lf\n", sum, previousSum);  
       previousSum = sum;
       i++;  
    }
}
int main()
{
    long double calculatedValue = expCalc(11);
    long double actualValue = exp(11);
    long double error = fabsl(calculatedValue - actualValue);
    printf("The calculated value is: %Lf\n", calculatedValue);
    printf("The actual value is: %Lf\n", actualValue);
    printf("The error in between is: %Lf\n", error);
}

And the output screenshot is: