1 - x <= exp(-x)

In [17]:

    

%matplotlib inline


    

In [22]:

    

import matplotlib.pyplot as plt


    

In [1]:

    

from math import exp


    

In [10]:

    

def f1(x): return 1 - x
def f2(x): return exp(-x)


    

In [11]:

    

vals = [1e-5, 1e-3, 1e-1, 1, 10, 100]


    

In [19]:

    

x_f1 = list(map(f1, vals))
x_f1


    

    
Out[19]:





[0.99999, 0.999, 0.9, 0, -9, -99]

In [20]:

    

x_f2 = list(map(f2, vals))
x_f2


    

    
Out[20]:





[0.9999900000499998,
 0.999000499833375,
 0.9048374180359595,
 0.36787944117144233,
 4.5399929762484854e-05,
 3.720075976020836e-44]

In [21]:

    

list(map(lambda x: f1(x) <= f2(x), vals))


    

    
Out[21]:





[True, True, True, True, True, True]

In [26]:

    

plt.plot(vals, x_f1);
plt.plot(vals, x_f2);


    

In [29]:

    

plt.plot(vals, [f2 - f1 for f1, f2 in zip(x_f1, x_f2)]);


    

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