File:Visualization of epsilon-delta-continuity 4.svg
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Size of this PNG preview of this SVG file: 720 × 540 pixels. Other resolutions: 320 × 240 pixels | 640 × 480 pixels | 1,024 × 768 pixels | 1,280 × 960 pixels | 2,560 × 1,920 pixels.
Original file (SVG file, nominally 720 × 540 pixels, file size: 16 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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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:44, 9 March 2017 | | 720 × 540 (16 KB) | wikimediacommons>Stephan Kulla | User created page with UploadWizard |
File usage
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