Pl. Let us remember that the exponential function can be written by the series i! i=0 In the present problem we will approach the concept of cancellation using as a case study the function ex. a. Write a python program that calculates the exponential function using the series given above. b. Assuming it is added in the order given, what stopping criterion should be used? c. Test your program for the numbers: x = 1,5,10,15,20 and also for x=-1, -5, -10, -15, -20. and compare your results for the python function numpy.exp (x). d. As you have just seen in the previous point, the written function can have undesirable effects when work with negative numbers. Use the relation e- x= 1/ex and compare the results. I What happens to the reliability of the function implemented in part a) when the terms of the sum are regrouped into even and odd numbers? Implement this new version of your program and Compare the results for the case of negative numbers