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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}]
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- 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.
|
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
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:31, 5 March 2011 | | 300 × 185 (39 KB) | Stpasha | 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 2010 |  | 288 × 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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