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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)

Summary

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

Mathematica source code

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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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.
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depicts

inception

7 August 2010

data size

39,990 byte

duration

16 second

height

185 pixel

width

300 pixel

media type

image/gif

checksum

fdc358b1ae51ffb16df0d927f15f6bfe9e3d709d

determination method or standard: SHA-1

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)StpashaAdd 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{{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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