This tutorial tells about LibreOffice Math in writing various mathematical limit equations. We explain them in 15 examples, including source code for each equation, and in the end you can download the .odf file containing all these limit equations. This tutorial is a continuation of the previous LibreOffice Math introduction.
Total Result
This is how it looks in LibreOffice Math program. You can download the .odf (OpenDocument Formula) file in the end of this tutorial. This .odf file contains all limit formulas mentioned in this tutorial.
Elements Toolbox
Where is limit templates in the Elements toolbox? It is in the Operators category.
The source code templates available for limit are:
- lim {}
- lim from{} {}
- lim to{} {}
- lim from{} to{} {}
Example 1
Source code:
lim from{ x->1^-"" } { {x^{2}-1} over {x-1} } = 2
Example 2
Source code:
lim from{ x->c } f( x ) = L
Example 3
Source code:
lim from{ x->3 } { {x^{2}-x-6 } over {x-3} } = lim from{ x->3 } { {(x-3)(x+2)} over {(x-3)} }
Example 4
Source code:
lim from{ x->9 } { {x-9} over {{sqrt{x}}-3} } = lim from{ x->9 } { {x-9} over {sqrt{x}-3} times {{sqrt{x}+3 } over {sqrt{x}+3 }} }
Example 5
Source code:
lim from{ x->0 } { sqrt{x^{2} - 2x + 3} }
Example 6
lim from{ x->2 } { left ( {{{6-x} over {x^{2} -4}} - {{1} over {x-2}} } right ) }
Example 7
sqrt{ {{lim from{x->5} x^{2}} + {lim from{x->5}11}} } over {lim from{x->5} x}
Example 8
lim from{ x->infinity } { 1 over x } = 0
Example 9
Source code:
lim from{ x->infinity } { {nroot{3}{x^{2}} - 2 {nroot{3}{x}} +1 } over {(x-1)^{2}} }
Example 10
A = lim csub{ <- csub{i in I} } A_{ i } = left lbrace {vec {a} in prod from{i in I} A_{i} divides a_{i} = f_{ij} (a_{j}) "for all" i <= j "in" I } right rbrace .
Example 11
Source code:
lim from{ n->infinity } { (a_{n} +- b_{n}) } = {lim from{ n->infinity } a_{n} } +- {lim from{ n->infinity } b_{ n }}
Example 12
Source code:
lim from{ n->infinity } { a^{p}_{n} } = left [ lim from{n->infinity} a_{n} right ]^p
Example 13
Source code:
lim from{ z->0 } {{ sin x } over {x}} = 1 newline newline newline
lim from{ x->0 } { {1-cos x} over {x} } = 0 newline newline newline
lim from{ z->infinity } { x sin (1 over x) } = 1 newline newline newline
Example 14
Source code:
lim from{ x->infinity } { int from{a} to{x} f(t) dt } newline newline newline
Example 15
lim from{ n->infinity } { sum from{i=8} to{n} f(s) } newline newline newline
Insert Formulas into Writer
To insert equations into LibreOffice Writer, you deal with the source codes. You will type the source code one by one per equation. And by selecting a source code > press Formula button, you change the source code into a beautiful formula automatically. Do this for all source codes left. See this picture.
Download
You can download the source file of those all limit expressions above as .odf (OpenDocument Formula) format here. Open it in LibreOffice Math; study, edit, and share it with anyone as you wish without any limitation.
https://archive.org/download/latihan-libreoffice/libreoffice-math-ubuntubuzz-limit.odf
References
- Diah Ayu & Sri Lestari, Matematika 2 untuk SMA/MA, Jakarta: Departemen Pendidikan Nasional, 2009.
- https://wiki.documentfoundation.org/images/a/a8/GS5109-GettingStartedWithMath.pdf
- https://wiki.documentfoundation.org/images/2/26/MG44-MathGuide.pdf
- https://en.wikipedia.org/wiki/Limit_function
- https://en.wikipedia.org/wiki/Inverse_limit
- https://en.wikipedia.org/wiki/Limit_of_a_sequence
- https://en.wikipedia.org/wiki/Limit_of_a_function