URGENT C PROGRAMMING

The function ex can be approximated by the summation of an infinite series:

_x² _x³ _x⁴

e^x =1+X++++

2! 3! 4!

1. Write a recursive function double power (double x, int n) that returns the result of xn.

(5 marks)

2. You are required to write the main function of the C program that can be used to evaluate ex using the infinite series. The program will terminate when the difference between the answer after n terms and the answer after n-1 terms s less than 10^-4. The program will take one command line argument: x that is the value of the parameter in ex. For example, if the user wants to determine ^e15, the following command can be invoked:

e.exe 1.5

The program will then evaluate the expression and display the result to standard output as shown below:

e^1.5000 = 4.4817

The program will also print an appropriate error message to standard error if the user does not provide the correct number of arguments to the program.

The program will call two functions: double fact (int n) that returns the factorial value of an integer as a double and double power (double x, int n) as written in part (a). Note that you do need to write the factorial function.