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Template:Limit

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alt = This template is under construction...
This template is under construction.            

Please do not use this unfinished and/or still unreliable template.            


The {{limit}} (or {{lim}}) mathematical formatting template is used to typeset limits in either HTML+CSS or LaTeX.

Usage

{{limit|subscript or underscript}} (format defaults to htm)

or

{{limit|subscript or underscript|format}}

or

{{limit|subscript or underscript|inf}} (format defaults to htm)

or

{{limit|subscript or underscript|inf|format}}

or

{{limit|subscript or underscript|sup}} (format defaults to htm)

or

{{limit|subscript or underscript|sup|format}}

where

  • the first parameter is the subscript or underscript;
  • the [optional] second parameter, is either inf (to get lim inf) or sup (to get lim sup), otherwise yields lim;
  • the [optional] last parameter (format), case insensitive, is either
  • htm: text style (subscript) HTML+CSS (default), or
  • HTM: display style (underscript) HTML+CSS, or
  • tex or TEX: LaTeX manages text style (subscript) and display style (underscript) automatically.

The template automatically converts -> to {{sp|1}}→ {{sp|1}} (HTML+CSS) or \to (LaTeX).

Examples

The code

{{indent}}before {{math|{{lim|''x''->0{{^|'''+'''}}}} ''x''{{^|0}}|tex = \lim_{x \to 0^+} x^0|&}}. Then

yields the text style HTML+CSS

     before
limx → 0+x 0
. Then

The code

{{indent}}before {{math|{{lim|''x''->0{{^|'''+'''}}}} ''x''{{^|0}}|tex = \lim_{x \to 0^+} x^0|$}}. Then

yields the text style LaTeX

     before . Then

The code

{{indent}}{{math|{{lim|''x''->0{{^|'''+'''}}|HTM}} ''x''{{^|0}}|tex = \lim_{x \to 0^+} x^0|&&}}

yields the display style HTML+CSS

     
x 0

The code

{{indent}}{{math|{{lim|''x''->0{{^|'''+'''}}|HTM}} ''x''{{^|0}}|tex = \lim_{x \to 0^+} x^0|$$}}

yields the display style LaTeX

     

The code

{{indent}}before {{math|{{lim|''x''->infty}} ''x''|tex = \lim_{x \to \infty} x|&}}. Then

yields the text style HTML+CSS

     before
limx → x
. Then

The code

{{indent}}before {{math|{{lim|''x''->infty}} ''x''|tex = \lim_{x \to \infty} x|$}}. Then

yields the text style LaTeX

     before . Then

The code

{{indent}}{{math|{{lim|''x''->infty|HTM}} ''x''|tex = \lim_{x \to \infty} x|&&}}

yields the display style HTML+CSS

     
x

The code

{{indent}}{{math|{{lim|''x''->infty|HTM}} ''x''|tex = \lim_{x \to \infty} x|$$}}

yields the display style LaTeX

     

The code

{{indent}}before {{math|{{lim|''n''->infty}} ''f'' {{sp|1}}(''n''), {{lim|''n''->infty|inf}} ''f'' {{sp|1}}(''n''), {{lim|''n''->infty|sup}} ''f'' {{sp|1}}(''n'')|&}}. Then

yields the text style HTML+CSS

     before 
limn → f  (n), lim infn → f  (n), lim supn → f  (n)
. Then

The code

{{indent}}before {{math|{{lim|''n''->infty|tex}} ''f''(''n''), {{lim|''n''->infty|inf|tex}} ''f''(''n''), {{lim|''n''->infty|sup|tex}} ''f''(''n'')|$}}. Then

yields the text style LaTeX

     before. Then

The code

{{indent}}{{math|{{lim|''n''->infty|HTM}} ''f'' {{sp|1}}(''n''),{{sp|quad}}{{lim|''n''->infty|inf|HTM}} ''f'' {{sp|1}}(''n''),{{sp|quad}}{{lim|''n''->infty|sup|HTM}} ''f'' {{sp|1}}(''n'').|&&}}

yields the text style HTML+CSS

     
f  (n), f  (n), f  (n).

The code

{{indent}}{{math|{{lim|''n''->infty|TEX}} ''f''(''n''),\quad {{lim|''n''->infty|inf|TEX}} ''f''(''n''),\quad {{lim|''n''->infty|sup|TEX}} ''f''(''n'').|$$}}

yields the text style LaTeX

     

The code

{{indent}}before {{math|{{lim|''n''->infty}} 1 {{op|+}} {{frac|1|''n''}} {{=}} 1|&}}. Then

yields the text style HTML+CSS

     before 
limn →   1  + 
1
n
= 1
. Then

The code

{{indent}}before {{math|{{lim|''n''->infty|tex}} 1 + {{frac|1|''n''|tex}} {{=}} 1|$}}. Then

yields the text style LaTeX

     before. Then

The code

{{indent}}{{math|{{lim|''n''->infty|HTM}} 1 {{op|+}} {{frac|1|''n''}} {{=}} 1.|&&}}

yields the display style HTML+CSS

     
  1 +
1
n
= 1.

The code

{{indent}}{{math|{{lim|''n''->infty|TEX}} 1 {{op|+}} {{frac|1|''n''|tex}} {{=}} 1.|$$}}

yields the display style LaTeX