File:Hopital sin x by -0.5x.png
From DawoumWiki, the free Mathematics self-learning
![File:Hopital sin x by -0.5x.png](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Hopital_sin_x_by_-0.5x.png/800px-Hopital_sin_x_by_-0.5x.png)
Size of this preview: 800 × 464 pixels. Other resolutions: 320 × 186 pixels | 640 × 371 pixels | 1,024 × 594 pixels | 1,666 × 966 pixels.
Original file (1,666 × 966 pixels, file size: 47 KB, MIME type: image/png)
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
Summary
Continuous completion of an example function quotient by l'Hôpital's rule, for example functions
and
:
At , the quotient is undefined since
. Defining the function as
completes the function definition such that a continuous function results, by l'Hôpital's rule.
Gnuplot source code |
---|
set style line 1 lc rgb "#ff8000" lw 3 # f
set style line 2 lc rgb "#ff0000" lw 3 # g
set style line 3 lc rgb "#a00000" lw 3 # f/g
set style line 4 lc rgb "#0060ff" lw 1.5 # f'
set style line 5 lc rgb "#0000ff" lw 1.5 # g'
set style line 8 lt 0 lc rgb "#000000" # major grid
set style line 9 lt 0 lc rgb "#e0e0e0" # minor grid
set title "Continuous completion of f(x)/g(x) by l'Hopital's rule"
set xlabel "x"
set ylabel "y"
set xrange [-6.5:6.5]
set yrange [-2.1:2.1]
set xtics 4
set ytics 1
set mxtics 4
set mytics 2
set grid xtics ytics mxtics mytics ls 8 , ls 9
plot sin(x) with lines ls 1 title "f(x) = sin(x)"
replot -0.5*x with lines ls 2 title "g(x) = -0.5x "
replot -sin(x)/(0.5*x) with lines ls 3 title "f(x)/g(x) "
replot cos(x) with lines ls 4 title "f'(x) "
replot -0.5 with lines ls 5 title "g'(x) "
set label at 0,-2 point pt 7 lc rgb "#a00000" pointsize 1.5 front
set label at 0,-2 point pt 7 lc rgb "#8080ff" pointsize 1.0 front
set label "defined as f'(0)/g'(0)" at 1.02,-2.05
set arrow from 1,-2.05 to 0.2,-2.01 filled
pause -1
|
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
![]() |
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
This file is licensed under the Creative Commons Attribution-Share Alike Attribution-Share Alike 4.0 International, 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic 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.
You may select the license of your choice.
![]() |
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}} .
It is recommended to name the SVG file “Hopital sin x by -0.5x.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
Captions
Example application of l'Hôpital's rule
Items portrayed in this file
depicts
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:44, 19 August 2016 | ![]() | 1,666 × 966 (47 KB) | wikimediacommons>Jochen Burghardt | Continuous completion of f(x)/g(x) by l'Hopital's rule |
File usage
The following page uses this file:
Retrieved from "https://dawoum.duckdns.org/wiki/File:Hopital_sin_x_by_-0.5x.png"