|1/x - 1/x0| ≤ |x0 - x| / x0^2 < ε .
def plot_function(): x = np.linspace(0.1, 10, 100) y = 1 / x
plt.plot(x, y) plt.title('Plot of f(x) = 1/x') plt.xlabel('x') plt.ylabel('f(x)') plt.grid(True) plt.show()
Let x0 ∈ (0, ∞) and ε > 0 be given. We need to find a δ > 0 such that
|x - x0| < δ .
Using the inequality |1/x - 1/x0| = |x0 - x| / |xx0| ≤ |x0 - x| / x0^2 , we can choose δ = min(x0^2 ε, x0/2) .
import numpy as np import matplotlib.pyplot as plt
|1/x - 1/x0| ≤ |x0 - x| / x0^2 < ε .
def plot_function(): x = np.linspace(0.1, 10, 100) y = 1 / x
plt.plot(x, y) plt.title('Plot of f(x) = 1/x') plt.xlabel('x') plt.ylabel('f(x)') plt.grid(True) plt.show()
Let x0 ∈ (0, ∞) and ε > 0 be given. We need to find a δ > 0 such that
|x - x0| < δ .
Using the inequality |1/x - 1/x0| = |x0 - x| / |xx0| ≤ |x0 - x| / x0^2 , we can choose δ = min(x0^2 ε, x0/2) .
import numpy as np import matplotlib.pyplot as plt
