Lesson 4

In the series of inequalities above, we used the standard inequality \[1 + x \le e^{x} \ \] which holds for all \(x \in \mathbb{R}\) and turns into equality only when \(x=0\). Let us recall what the graphs of these two functions look like.

import matplotlib.pyplot as plt
import numpy as np


x = np.linspace(-3, 3, 100)
plt.plot(x, np.exp(x), label='$e^x$')
plt.plot(x, x + 1, label='$x+1$')
plt.legend(loc='upper left')
plt.savefig('exp.png')