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$$ f(x) = \frac{1}{x} $$
In [1]:
import math
In [2]:
def exp_taylor(x, n):
    c = 1.0
    f = 1.0
    for i in range(n):
        c /= (i+1)
        f += c * x**(i+1)
    return f
In [3]:
x = 0.5
print('x     = ', x)
print('1st   = ', exp_taylor(x, 1))
print('2nd   = ', exp_taylor(x, 2))
print('3rd   = ', exp_taylor(x, 3))
print('4th   = ', exp_taylor(x, 4))
print('5th   = ', exp_taylor(x, 5))
print('6th   = ', exp_taylor(x, 6))
print('7th   = ', exp_taylor(x, 7))
print('8th   = ', exp_taylor(x, 8))
print('exact = ', math.exp(x))

x     =  0.5
1st   =  1.5
2nd   =  1.625
3rd   =  1.6458333333333333
4th   =  1.6484375
5th   =  1.6486979166666667
6th   =  1.6487196180555554
7th   =  1.6487211681547618
8th   =  1.6487212650359622
exact =  1.6487212707001282
In [4]:
# numpy
import numpy as np

# matplotlibのおまじない
from matplotlib import pylab as plt

x = np.linspace(0.0, np.pi, 100)
y = np.cos(x)**2
plt.plot(x, y)
Out[4]:
[<matplotlib.lines.Line2D at 0x7fc02c1c73d0>]
In [ ]: