File:Visualization of epsilon-delta-continuity 1.svg
| Uploaded by | Stephan Kulla |
|---|---|
| Upload date | 2017-02-13T23:48:06Z |
| MIME type | image/svg+xml |
| Dimensions | 720 × 540 px |
| File size | 15.6 KB |
Summary
| Description |
English: Visualization of the epsilon-delta-continuity with the function and the point . The 2epsilon-2delta-rectangle is drawn with and . |
| Date | |
| Source | Own work |
| Author | Stephan Kulla (User:Stephan Kulla) |
| Other versions |
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| SVG development |  This plot was created with Matplotlib. |
| Source code | Python codefrom matplotlib.patches import Rectangle
import matplotlib.pyplot as plt
import numpy as np
def create_plot(f, xs, x0, eps, delta, filename):
ys = f(xs)
y0 = f(x0)
xmin = xs.min()
ymin = ys.min()
xss = xs[(xs > x0-delta) & (xs < x0+delta)]
yss = f(xss)
sg = (yss > y0-eps) & (yss < y0+eps)
fig, ax = plt.subplots(1,1)
ax.add_patch(
Rectangle((x0-delta,y0-eps), 2*delta, 2*eps, edgecolor="black",
alpha=0.6, linestyle="solid", facecolor="#dddddd", lw=1.5))
ax.plot(xs, ys)
yss[~sg] = None
ax.plot(xss, yss, color="green", lw=2)
yss = f(xss)
yss[sg] = None
ax.plot(xss, yss, color="red", lw=2)
ax.plot([x0], [y0], "o", color="black")
fig.savefig(filename)
xs = np.linspace(-2, 4, 1e5)
create_plot(lambda x: x/3.0, xs, 1, 1, 2, "Visualization of epsilon-delta-continuity 1.svg")
create_plot(lambda x: x/3.0, xs, 1, 0.5, 1, "Visualization of epsilon-delta-continuity 2.svg")
create_plot(lambda x: x/3.0, xs, 1, 1./3, 3./4, "Visualization of epsilon-delta-continuity 3.svg")
create_plot(lambda x: x/3.0, xs, 1, 0.5, 2, "Visualization of epsilon-delta-continuity 4.svg")
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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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