C Exercises: Calculate e raise to the power x using sum of first n terms of Taylor Series

C Programming Mathematics: Exercise-24 with Solution

Write a C program to calculate e raised to the power of x using the sum of the first n terms of the Taylor Series.

From Wikipedia,
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
Example:
The Taylor series for any polynomial is the polynomial itself.

The above expansion holds because the derivative of e^x with respect to x is also e^x, and e⁰ equals 1.
This leaves the terms (x − 0)ⁿ in the numerator and n! in the denominator for each term in the infinite sum.

Example:
Input: n = 25
float x = 5.0
Output: e^x = 148.413162

Sample Solution:

C Code:

#include <stdio.h>
#include <stdlib.h>

 float Taylor_exponential(int n, float x) 
    { 
        float exp_sum = 1;     
        for (int i = n - 1; i > 0; --i ) 
            exp_sum = 1 + x * exp_sum / i;    
        return exp_sum; 
    } 
  int main(void)
    {  
       int n = 25;
       float x = 5.0;    
       
       if (n>0 && x>0)
		{	
		 printf("value of n = %d and x = %d ", n, x );
		 printf("\ne^x = %f",Taylor_exponential(n,x)); 
		}         
   }

Sample Output:

value of n = 25 and x = 1968710504 
e^x = 148.413162

Flowchart:

C Programming Code Editor:

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