File:Dependence of delta with epsilon in case of the continuous square function.svg
Summary
| Description |
English: Illustration of the dependence of epsilon and delta for the epsilon-delta-criterion of continuity. The function is shown. is continuous at . |
| Date | |
| Source | Own work |
| Author | Stephan Kulla (User:Stephan Kulla) |
| SVG development | |
| Source code | Python codeimport matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Rectangle
from itertools import chain
ax, fig = plt.subplots(1,4)
xs = np.linspace(0.0, 1.5, 1e4)
ys = xs*xs
ax.set_figwidth(20)
ax.set_figheight(4)
epsilons = [0.8, 0.6, 0.4, 0.2]
for f, eps in zip(fig, epsilons):
delta = eps/3
f.plot(xs, ys)
f.set_ylim((0,2))
f.set_xlim((0,2))
f.add_patch(Rectangle((1-delta,1-eps), 2*delta, 2*eps,
edgecolor="black", facecolor="#dddddd",
alpha=0.6, linestyle="solid", lw=1.5))
xs_delta = xs[(xs > 1-delta) & (xs < 1+delta)]
f.plot(xs_delta, xs_delta*xs_delta, color="green", lw=3)
f.plot([1], [1], "o", color="black")
ax.savefig("Dependence of delta with epsilon in case of the continuous square function.svg", bbox_inches='tight', pad_inches=0.5)
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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