Image:LogTay.svg

[edit] Summary

 note that, for x > 1, the successive approximations grow worse

[edit] 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

[edit] Licensing

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. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | 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 | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-

• Natural logarithm
• Taylor series