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This is a file from the Wikimedia Commons. The description on its description page there is shown below.Commons is a freely licensed media file repository. You can help.
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Summary
Description |
log(1+x) and Taylor approximations of degree 4, 7, 11, 16
note that, for x > 1, the successive approximations grow worse
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Source |
self-made |
Date |
3/4/2008 |
Author |
Niles |
Permission ( Reusing this image) |
Public domain
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Instructions
Created with gnuplot using the following code
set terminal svg \
size 1000 1000 \
fixed enhanced \
fname 'Times' \
fsize 22
set output "LogTay.svg"
set samples 2000
set autoscale fix
set xrange [-1.5:1.5]
set yrange [-4:2]
set grid
set xtics .5
set ytics .5
set xzeroaxis linewidth 2.5
set yzeroaxis linewidth 2.5
set key -.5,1.5
unset border
plot x - x**2/2 + x**3/3 - x**4/4 lw 2 title "T_4", \
x - x**2/2 + x**3/3 - x**4/4 + x**5/5 - x**6/6 + x**7/7 lw 2 title "T_7", \
x - x**2/2 + x**3/3 - x**4/4 + x**5/5 - x**6/6 + x**7/7 -x**8/8 + \
x**9/9 - x**10/10 + x**11/11 lw 2 title "T_{11}", \
x - x**2/2 + x**3/3 - x**4/4 + x**5/5 - x**6/6 + x**7/7 -x**8/8 + \
x**9/9 - x**10/10 + x**11/11 - x**12/12 + x**13/13-x**14/14 + \
x**15/15 - x**16/16 lw 2 title "T_{16}", \
log(1+x) lw 3 lt 7
Licensing
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I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
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File history
Click on a date/time to view the file as it appeared at that time.
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Date/Time |
Dimensions |
User |
Comment |
current |
14:13, 5 March 2008 |
1,000×1,000 (127 KB) |
Nilesj |
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23:56, 4 March 2008 |
1,000×1,000 (127 KB) |
Nilesj |
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23:56, 4 March 2008 |
1,000×1,000 (62 KB) |
Nilesj |
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23:51, 4 March 2008 |
1,000×1,000 (62 KB) |
Nilesj |
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18:32, 4 March 2008 |
1,000×1,000 (127 KB) |
Nilesj |
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File links
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