Image:LogTay.svg

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LogTay.svg‎ (SVG file, nominally 1,000 × 1,000 pixels, file size: 127 KB)

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Summary

Description

log(1+x) and Taylor approximations of degree 4, 7, 11, 16

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

self-made

Date

3/4/2008

Author

Niles

Permission
( Reusing this image)

Public domain


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

Licensing

Public domain
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.


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File history

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

Date/Time Dimensions User Comment
current 14:13, 5 March 2008 1,000×1,000 (127 KB) Nilesj (typo in the original file mis-labeled one of the graphs; T_16 is now correctly labeled)
23:56, 4 March 2008 1,000×1,000 (127 KB) Nilesj (Reverted to version as of 18:32, 4 March 2008)
23:56, 4 March 2008 1,000×1,000 (62 KB) Nilesj
23:51, 4 March 2008 1,000×1,000 (62 KB) Nilesj
18:32, 4 March 2008 1,000×1,000 (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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