Original file (996 × 509 pixels, file size: 46 KB, MIME type: image/png)

Captions

Captions

Add a one-line explanation of what this file represents

Summary

edit

Made by myself with matlab.

File:LimSup.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.

File:LimSup.png → File:LimSup.svg

For more information, see Help:SVG.

In other languages
Alemannisch  Bahasa Indonesia  Bahasa Melayu  British English  català  čeština  dansk  Deutsch  eesti  English  español  Esperanto  euskara  français  Frysk  galego  hrvatski  Ido  italiano  lietuvių  magyar  Nederlands  norsk bokmål  norsk nynorsk  occitan  Plattdüütsch  polski  português  português do Brasil  română  Scots  sicilianu  slovenčina  slovenščina  suomi  svenska  Tiếng Việt  Türkçe  vèneto  Ελληνικά  беларуская (тарашкевіца)  български  македонски  нохчийн  русский  српски / srpski  татарча/tatarça  українська  ქართული  հայերեն  বাংলা  தமிழ்  മലയാളം  ไทย  한국어  日本語  简体中文  繁體中文  עברית  العربية  فارسی  +/−
New SVG image

Licensing

edit
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.


Source code (MATLAB)

edit
function main() % draw an illustration for limit superior and limit inferior

% prepare the screen and define some parameters   
clf; hold on; axis equal; axis off; 
fontsize=25; thick_line=3; thin_line=2;
black=[0, 0, 0]; red=[1, 0, 0]; blue=[0, 0, 1];
arrowsize=0.5; arrow_type=1; arrow_angle=30; % (angle in degrees)
circrad=0.07; % radius of ball showing up in places


B=9.4;
X=0:0.05:B;

f=inline('(X+2)./(X+0.9)', 'X');
Y=sin(5*X).*f(X);

for i=1:length(X)
   ball(X(i), Y(i), circrad, blue);
end

K=1.5;
X=0:0.05:(B+K);
Z=f(X);
plot(X, Z, 'r--', 'linewidth', thin_line)
plot(X, -Z, 'r--', 'linewidth', thin_line)

L=f(B); 
plot([B+0.4*K B+K], [L, L], 'linestyle', '-', 'linewidth', thick_line, 'color', red);
plot([B+0.4*K B+K], [-L, -L], 'linestyle', '-', 'linewidth', thick_line, 'color', red);

shift=2*K;
H=text(B+shift, L,  'lim sup');          set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'c')
H=text(B+shift, -L,  'lim inf');          set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'c')

shift=-3;
K1=1.2; K2=2.6; 
arrow([-1 shift], [K1*B, shift],          thin_line, arrowsize, arrow_angle, arrow_type, black) 
arrow([-1, shift], [-1, K2*L],            thin_line, arrowsize, arrow_angle, arrow_type, black) 

axis ([-0.2*B, K1*B+1, -2*L+shift, K2*L]);

H=text(K1*B+0.6, shift,  '\it{n}');          set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'c')
H=text(-1, K2*L+0.5,  '\it{x_n}');          set(H, 'fontsize', fontsize, 'HorizontalAlignment', 'c')

saveas(gcf, 'LimSup.eps', 'psc2') % export to eps

function ball(x, y, r, color)
   Theta=0:0.1:2*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, color);
   set(H, 'EdgeColor', 'none');


function arrow(start, stop, thickness, arrow_size, sharpness, arrow_type, color)
   
% Function arguments:
% start, stop:  start and end coordinates of arrow, vectors of size 2
% thickness:    thickness of arrow stick
% arrow_size:   the size of the two sides of the angle in this picture ->
% sharpness:    angle between the arrow stick and arrow side, in degrees
% arrow_type:   1 for filled arrow, otherwise the arrow will be just two segments
% color:        arrow color, a vector of length three with values in [0, 1]
   
% convert to complex numbers
   i=sqrt(-1);
   start=start(1)+i*start(2); stop=stop(1)+i*stop(2);
   rotate_angle=exp(i*pi*sharpness/180);

% points making up the arrow tip (besides the "stop" point)
   point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);
   point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);

   if arrow_type==1 % filled arrow

      % plot the stick, but not till the end, looks bad
      t=0.5*arrow_size*cos(pi*sharpness/180)/abs(stop-start); stop1=t*start+(1-t)*stop;
      plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', thickness, 'Color', color);

      % fill the arrow
      H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);
      set(H, 'EdgeColor', 'none')
      
   else % two-segment arrow
      plot(real([start, stop]), imag([start, stop]),   'LineWidth', thickness, 'Color', color); 
      plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', thickness, 'Color', color);
      plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', thickness, 'Color', color);
   end

File history

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

Date/TimeThumbnailDimensionsUserComment
current17:02, 24 February 2007Thumbnail for version as of 17:02, 24 February 2007996 × 509 (46 KB)Oleg Alexandrov (talk | contribs)Made by myself with matlab.

There are no pages that use this file.

File usage on other wikis

The following other wikis use this file: