Image:LogTay.svg
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LogTay.svg (SVG file, nominally 1,000 × 1,000 pixels, file size: 127 KB)
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This is a file from the Wikimedia Commons. The description on its description page there is shown below. |
Summary
| Description |
log(1+x) and Taylor approximations of degree 4, 7, 11, 16 note that, for x > 1, the successive approximations grow worse |
|---|---|
| Source |
self-made |
| Date |
3/4/2008 |
| Author |
Niles |
| Permission ( Reusing this image) |
Public domain
|
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: Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Cebuano | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | Norsk (bokmål) | Norsk (nynorsk) | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Suomi | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | 中文(简体) | 中文(繁體) | zh-yue-hant | +/- |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 14:13, 5 March 2008 | 1,000×1,000 (127 KB) | Nilesj | (typo in the original file mis-labeled one of the graphs; T_16 is now correctly labeled) |
| 23:56, 4 March 2008 | 1,000×1,000 (127 KB) | Nilesj | (Reverted to version as of 18:32, 4 March 2008) | |
| 23:56, 4 March 2008 | 1,000×1,000 (62 KB) | Nilesj | ||
| 23:51, 4 March 2008 | 1,000×1,000 (62 KB) | Nilesj | ||
| 18:32, 4 March 2008 | 1,000×1,000 (127 KB) | Nilesj | ({{Information |Description=log(1+x) and Taylor approximations of degree 4, 7, 11, 13 |Source=self-made |Date=3/4/2008 |Author= Niles |Permission=Public domain |other_versions= }} ) |
