File:Taylor approximation of natural logarithm.gif

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Taylor_approximation_of_natural_logarithm.gif (300 × 185 pixels, file size: 39 KB, MIME type: image/gif, looped, 12 frames, 16 s)

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Summary

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Description
English: animation showing the Taylor series of the natural logarithm at x=1
Date
Source Own work
Author Jakob.scholbach

Mathematica source code

[edit]
g2 = Table[
  Plot[{Log[z], Sum[-(1 - z)^n/n, {n, 1, k}]},
   {z, 0, 5},
   ImageSize -> 300,
   Ticks -> {{1, 2, 4}, {-2, -1, 0, 1, 3}},
   AxesStyle -> 
    Directive[FontSize -> 12, FontFamily -> "Arial", Gray],
   AxesLabel -> {"\!\(\*
StyleBox[\"x\",\nFontSlant->\"Italic\"]\)", "ln(\!\(\*
StyleBox[\"x\",\nFontSlant->\"Italic\"]\))"},
   PlotStyle -> {{Black, Thickness[0.003]},
     {RGBColor[0, 0.5, 0.2], Thickness[.015]}},
   PlotRange -> {{0, 3}, {-3, 2}},
   Epilog -> {
     FontSize -> 12, FontFamily -> "Arial",
     Inset["k = " <> ToString[k], {0.8, 1.2}]
     }],
  {k, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 99, 100}}]
Export["Taylor_approximation_of_natural_logarithm.gif", g2, 
 "DisplayDurations" -> {.4, 1, 1, 1, 1, 1, 1, 1, 1, .5, 1}]

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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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.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

File history

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Date/TimeThumbnailDimensionsUserComment
current03:31, 5 March 2011Thumbnail for version as of 03:31, 5 March 2011300 × 185 (39 KB)Stpasha (talk | contribs)Add labels, made the Taylor approximation line more pronounced, added two more steps with large k's: k=99 and k=100 (almost the limiting case), font for labels converted into Arial to match the font used by the article.
10:15, 7 August 2010Thumbnail for version as of 10:15, 7 August 2010288 × 177 (14 KB)Jakob.scholbach (talk | contribs){{Information |Description={{en|1=animation showing the Taylor series of the natural logarithm at x=1 Mathematica source code <nowiki> Table[Plot[{ Log[z], Sum[-(1 - z)^n/n, { n, 1, k}]}, {z, 0, 3}, PlotStyle -> {{Thickness[.01], RGBColor[

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