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File:LogTay.svg

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Summary

Description
English: The log(x+1) and Taylor approximations of degree 4, 7, 11, 16. Note that, for x > 1, the successive approximations grow worse.
العربية: الدالة log(x+1) وتقريبات تايلور من الدرجة 4، 7، 11، 16. التقريبات تكون سيئة من أجل x > 1.
Date
Source Own work
Author Niles
Permission
(Reusing this file)		 Public domain

Instructions

Created with gnuplot using the following code 

set terminal svg \
        size 1000 1000 \
        fixed enhanced \
        fname 'Times New Roman'  \
        fsize 32

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 -0.1,1.75
        
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

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Captions

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inception

4 March 2008

data size

131,032 byte

height

1,000 pixel

width

1,000 pixel

media type

image/svg+xml

checksum

12ba9fb999f849efb234480da2483a4048ce3e91

determination method or standard: SHA-1

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current23:27, 30 November 2009Thumbnail for version as of 23:27, 30 November 20091,000 × 1,000 (128 KB)PlasticsporkIncreased fontsize
20:20, 29 November 2009Thumbnail for version as of 20:20, 29 November 20091,000 × 1,000 (128 KB)PlasticsporkChanged font from Times to Times New Roman
14:13, 5 March 2008Thumbnail for version as of 14:13, 5 March 20081,000 × 1,000 (127 KB)Nilesjtypo in the original file mis-labeled one of the graphs; T_16 is now correctly labeled
23:56, 4 March 2008Thumbnail for version as of 23:56, 4 March 20081,000 × 1,000 (127 KB)NilesjReverted to version as of 18:32, 4 March 2008
23:56, 4 March 2008Thumbnail for version as of 23:56, 4 March 20081,000 × 1,000 (62 KB)Nilesj
23:51, 4 March 2008Thumbnail for version as of 23:51, 4 March 20081,000 × 1,000 (62 KB)Nilesj
18:32, 4 March 2008Thumbnail for version as of 18:32, 4 March 20081,000 × 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= }}

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