Please help me with this question in Python.

#===========================================================

def myexp_pos(x, tol=10**(-10)): ''' Input x is nonnegative real, compute exp(x) using Taylor series '''

#=========================================================== def myexp_neg(x, tol=10**(-10)): ''' Input x is negative real, compute exp(x) using Taylor series. (The three returned values exp1, exp2, exp3 are computed using formulas specified in the project pdf file.) '''

return (exp1, exp2, exp3)

#=========================================================== if __name__=='__main__': import math import numpy as np

tol = 10**(-12)

for x in np.arange(0.0, 30.0, 0.5): myexp = myexp_pos(x, tol) mathexp = math.exp(x) absolute_error = abs(mathexp - myexp) relative_error = abs(mathexp - myexp)/mathexp print('exp({:6.2f})={:14.10e}, your_exp={:14.10e}, abs_err={:10.5e}, rel_err={:14.10e}'. format(x, mathexp, myexp, absolute_error, relative_error)) if abs(relative_error) > tol: print("Too large error from myexp_pos(), implementation can be wrong")

for x in list(np.arange(-60.0, -25.0, 2.0))+list(np.arange(-25.0, 0.)): (exp1, exp2, exp3) = myexp_neg(x, tol) mathexp = math.exp(x) errorV = [ abs(mathexp - expx) for expx in (exp1, exp2, exp3) ] print(' exp({:6.2f})={:14.10e}'.format(x, mathexp)), print('exp1={:14.10e}, exp2={:14.10e}, exp3={:14.10e}'.format(exp1,exp2,exp3)) print('err1={:14.10e}, err2={:14.10e}, err3={:14.10e}'.format(errorV[0], errorV[1], errorV[2]))

## ## there is no pass or fail test in the problem, from the printed out errors above you can ## try to make sense of if your code is implemented correctly. ## ## among exp1, exp2, exp3, one of them should be consistently having large error (because ## numerical cancelation error makes the summation scheme unreliable). you'll need to find ## out which one is the least accurate by looking at your numerical results from the above tests. ##