import numpy as np
from numpy import pi
from numpy.linalg import solve, norm    # Solve linear systems and compute norms
import matplotlib.pyplot as plt

newparams = {'figure.figsize': (6.0, 6.0), 'axes.grid': True,
             'lines.markersize': 8, 'lines.linewidth': 2,
             'font.size': 14}
plt.rcParams.update(newparams)



# Exercise 0
f = lambda x: x**3-1
g = lambda y: 3*x**2

x = 3
for i in range(7):
    x = x - f(x)/g(x)
    print(np.abs(x-1))

"""
Output:
1.0370370370370372
0.4383552698704216
0.12002238333650928
0.012402260381869423
0.00015131136058266215
2.2890509709938556e-08
4.440892098500626e-16
"""