meyers hw 14.ipynb

Kernel: SageMath 8.2

import numpy as np

def func(x):
    return sin(x) - cos(x)

plot(func(x),(x,-2*pi,2*pi))
h = [.1,.01,.001,.0001,.00001,.000001,.00000001,.000000001,.000000001,.00000000001,.000000000001,.00000000001,.0000000000001]

np.set_printoptions(precision=2)
x =0
for width in h:
    print((f(x+width)-f(x))/(2*width))

0.524146256844011
0.502491645875069
0.500249916645823
0.500024999166571
0.500002499992380
0.500000250036603
0.500000002512380
0.499999985859034
0.499999985859034
0.500000041370185
0.499988939139939
0.500000041370185
0.500155472593633

# The error decreases to a point, but then begins to increase due to the periodic nature of the function