File:The continuosly differentiably in irrational and discontinuosly differentiably in rational function.svg
![File:The continuosly differentiably in irrational and discontinuosly differentiably in rational function.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/The_continuosly_differentiably_in_irrational_and_discontinuosly_differentiably_in_rational_function.svg/576px-The_continuosly_differentiably_in_irrational_and_discontinuosly_differentiably_in_rational_function.svg.png?20211011062912)
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Summary
[edit]DescriptionThe continuosly differentiably in irrational and discontinuosly differentiably in rational function.svg |
English: Graphic of
where |
Date | |
Source | Own work |
Author | Arami Mira |
SVG development InfoField | ![]() This diagram was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
import math
from fractions import Fraction
def nextPair(x, y):
a = x
b = y
if (a + b) % 2 == 0:
a -= 1
b += 1
if a == 0:
a = 1
else:
a += 1
b -= 1
if b == 0:
b = 1
return a, b
def nextRational(x):
if x == 0:
return Fraction(1, 1)
n = x.numerator
d = x.denominator
n, d = nextPair(n, d)
while math.gcd(n, d) != 1:
n, d = nextPair(n, d)
return Fraction(n, d)
def seriesFunction(center, x):
return 0 if x == center else (x-center)*(x-center)*math.sin(1/(x-center))
def series(n, x):
q = 1.1
f = 1
s = 0
r = Fraction(0, 1)
for i in range(n):
s += (seriesFunction(r, x)) / f
if (i > 0):
s += (seriesFunction(-r, x)) / f
f *= q
r = nextRational(r)
return s - 20*x
x = np.linspace(-2.1, 2.1, 5000)
y = [series(100, i) for i in x]
f, ax = plt.subplots()
ax.set_xlim(-2, 2)
plt.plot(x, y)
plt.savefig("The continuosly differentiably in irrational and discontinuosly differentiably in rational function.svg")
|
Licensing
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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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 06:29, 11 October 2021 | ![]() | 576 × 432 (24 KB) | Arami Mira (talk | contribs) | Uploaded own work with UploadWizard |
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Width | 460.8pt |
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Height | 345.6pt |