File:Discontinuity of function sin(1 over x).svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 575 × 431 pixels, file size: 303 KB)

Captions

Captions

Add a one-line explanation of what this file represents

Summary[edit]

Description
English: Illustration of the discontinuity of the function . The graph is shown together with the points with (green) and the point (orange).
Date
Source Own work
Author Stephan Kulla (User:Stephan Kulla)
Other versions
  • Graph of function sin(1 over x)
    Graph of function sin(1 over x)
  • Discontinuity of function sin(1 over x) with sequence criterion
    Discontinuity of function sin(1 over x) with sequence criterion
  • Discontinuity of function sin(1 over x) with epsilon-delta criterion
    Discontinuity of function sin(1 over x) with epsilon-delta criterion
  • Graph of function x*sin(1 over x)
    Graph of function x*sin(1 over x)
  • Graph of function x^2*sin(1 over x)
    Graph of function x^2*sin(1 over x)
SVG development
InfoField
 
The SVG code is valid.
 
This plot was created with Matplotlib.
Source code
InfoField

Python code

import matplotlib.pyplot as plt
import numpy as np

from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes, mark_inset

blue="#007ec1"
orange="#d77a5a"
green="#6e8334"

def f(x):
    return np.sin(1/x)

xs1 = np.linspace(-3, 3, 10001)
xs2 = 1/(np.arange(1., 1001, 1.) * np.pi/2)

xs = np.union1d(np.union1d(xs1,xs2),-xs2)

xns = 1 / (2 * np.arange(0., 1000, 1) * np.pi + np.pi/2)

fig, ax = plt.subplots()

ax.plot(xs, f(xs), color=blue)
ax.plot(xns, f(xns), "o", color=green)
ax.plot([0],[0],"o", markerfacecolor="white", color="black")
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.1, 1.1)

axins = zoomed_inset_axes(ax, 20, loc=4)
axins.plot(xs, f(xs))
axins.plot(xns, f(xns), "o", color=green)
axins.set_xlim(-0.0, 0.05)
axins.set_ylim(0.98, 1.01)

mark_inset(ax, axins, loc1=1, loc2=3, fc="0.95", ec="0.7")

plt.xticks(visible=False)
plt.yticks(visible=False)

plt.savefig("Discontinuity of function sin(1 over x).svg")

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:27, 21 May 2018Thumbnail for version as of 18:27, 21 May 2018575 × 431 (303 KB)Stephan Kulla (talk | contribs)update
18:57, 27 March 2017Thumbnail for version as of 18:57, 27 March 2017720 × 540 (357 KB)Stephan Kulla (talk | contribs)bigger dots
18:44, 27 March 2017Thumbnail for version as of 18:44, 27 March 2017720 × 540 (357 KB)Stephan Kulla (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

File usage on other wikis

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Discontinuity_of_function_sin(1_over_x).svg&oldid=460159483"