import numpy as np import matplotlib.pyplot as plt
|1/x - 1/x0| ≤ |x0 - x| / x0^2 < ε .
Using the inequality |1/x - 1/x0| = |x0 - x| / |xx0| ≤ |x0 - x| / x0^2 , we can choose δ = min(x0^2 ε, x0/2) . mathematical analysis zorich solutions
Then, whenever |x - x0| < δ , we have
|1/x - 1/x0| < ε
import numpy as np import matplotlib.pyplot as plt
|1/x - 1/x0| ≤ |x0 - x| / x0^2 < ε .
Using the inequality |1/x - 1/x0| = |x0 - x| / |xx0| ≤ |x0 - x| / x0^2 , we can choose δ = min(x0^2 ε, x0/2) .
Then, whenever |x - x0| < δ , we have
|1/x - 1/x0| < ε