# 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 e^{0} 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>
// Function to calculate the exponential function using Taylor series approximation
float Taylor_exponential(int n, float x) {
float exp_sum = 1; // Initialize the sum as 1 (initial term of Taylor series)
// Loop to calculate each term of the Taylor series for the exponential function
for (int i = n - 1; i > 0; --i) {
exp_sum = 1 + x * exp_sum / i; // Calculate the next term of the series and update the sum
}
return exp_sum; // Return the final result of the Taylor series approximation for e^x
}
// Main function
int main(void) {
int n = 25; // Number of terms for Taylor series
float x = 5.0; // Value of x in e^x
// Check if n and x are greater than 0 before proceeding
if (n > 0 && x > 0) {
printf("value of n = %d and x = %f ", n, x);
printf("\ne^x = %f", Taylor_exponential(n, x)); // Calculate and print the result of e^x
}
return 0;
}
```

Sample Output:

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

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