In numerical methods, one source of error occurs when we use an approximation for a mathematical expression that would otherwise be too costly to compute in terms of run-time or memory resources. One routine example is the approximation of infinite series by a finite series that mostly captures the important behavior of the infinite series. In this problem you will implement an approximation to the exp(x) as represented by the following infinite series,
exp(x) = Infinity n= 0 xn/xn!
Your approximation will be a truncated finite series with N + 1 terms,
exp(x, N) = Infinityn n = 0 xn/xn!
For the first part of this problem, you are given a random real number x and will investigate how well a finite series expansion for exp(x) approximates the infinite series.
Compute exp(x) using a finite series approximation with N E [0, 9] N (i. e. is an integer).
Save the 10 floating point values from your approximation in a numpy array named exp_approx. exp_approx should be of shape (10,) and should be ordered with increasing N (i. e. the first entry of exp_approx should correspond to exp(x, N) when N = 0 and the last entry when N = 9).