File:Logarithm GIF.gif
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Logarithm_GIF.gif (800 × 600 pixels, file size: 368 KB, MIME type: image/gif, looped, 14 frames, 14 s)
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Summary[edit]
| Description |
English: log(x+1) and its Taylor approximation. It shows Taylor approximation has certain limitations over some intervals. العربية: الدالة log(x+1) وتقريب تايلور الخاص بها. يبين أن تقريب تايلور له فترة محددة. |
| Date | |
| Source | Own work |
| Author | IkamusumeFan |
Matplotlib (Python)[edit]
import math as m
import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
# import matplotlib.animation as animation
def draw_frame(n,filename,line_color):
fig = plt.figure()
plt.axes([0.02,0.13,0.9,0.8])
plt.hold(True)
plt.xlim(-1.5,1.5)
plt.ylim(-4,2)
# Set up the spines
ax = plt.gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))
# Set up the label
ax.text(0.5,-2,'N='+str(n),fontsize=24,color=line_color)
Q = []
# Draw the original function (ORG) curve
X = np.arange(-0.999, 1.5, 0.001)
ORG = np.log(X+1)
a = plt.plot(X, ORG, '-', color='black', lw=3)
Q.append(a)
# Draw the approximation function (APPR) curve
X = np.arange(-1.5, 1.5, 0.001)
i=1
APPR = (-1)**(i+1)*(X**i)/i
while (i<n):
i = i+1
APPR = APPR+(-1)**(i+1)*(X**i)/i
a = plt.plot(X, APPR, '-', color=line_color, lw=3)
Q.append(a)
plt.savefig(filename)
draw_frame(1,'frame01.jpg','#b30000')
draw_frame(2,'frame02.jpg','#00b300')
draw_frame(3,'frame03.jpg','#0000b3')
draw_frame(4,'frame04.jpg','#b3b300')
draw_frame(5,'frame05.jpg','#00b3b3')
draw_frame(6,'frame06.jpg','#b300b3')
draw_frame(7,'frame07.jpg','#b3b3b3')
draw_frame(8,'frame08.jpg','#3300b3')
draw_frame(9,'frame09.jpg','#33b300')
draw_frame(10,'frame10.jpg','#0033b3')
draw_frame(15,'frame11.jpg','#b3b333')
draw_frame(20,'frame12.jpg','#334433')
draw_frame(45,'frame13.jpg','#ff0000')
draw_frame(100,'frame14.jpg','#0000ff')
# To generate the final GIF file, use the shell command:
# convert -antialias -loop 0 -delay 100 -compress LZW frame* Logarithm_GIF.gif
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:19, 26 August 2013 | | 800 × 600 (368 KB) | IkamusumeFan (talk | contribs) | User created page with UploadWizard |
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