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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2022-1-C2-formulas-defs.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2022-1-C2-formulas-defs.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2022-1-C2-formulas-defs.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2022-1-C2-formulas-defs.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2022-1-C2-formulas-defs.pdf"))
% (defun ed () (interactive) (find-LATEX "2022-1-C2-formulas-defs.tex"))
% (defun et () (interactive) (find-LATEX "2022-1-C2-formulas-test.tex"))
% (defun o () (interactive) (find-LATEX "2022-1-C2-formulas-defs.tex"))
% (defun u () (interactive) (find-latex-upload-links "2022-1-C2-formulas-defs"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2022-1-C2-formulas-defs.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (code-eec-LATEX "2022-1-C2-formulas-defs")
% (find-pdf-page "~/LATEX/2022-1-C2-formulas-defs.pdf")
% (find-sh0 "cp -v ~/LATEX/2022-1-C2-formulas-defs.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2022-1-C2-formulas-defs.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2022-1-C2-formulas-defs.pdf")
% file:///home/edrx/LATEX/2022-1-C2-formulas-defs.pdf
% file:///tmp/2022-1-C2-formulas-defs.pdf
% file:///tmp/pen/2022-1-C2-formulas-defs.pdf
% http://angg.twu.net/LATEX/2022-1-C2-formulas-defs.pdf
% (find-LATEX "2019.mk")
% (find-sh0 "cd ~/LUA/; cp -v Pict2e1.lua Pict2e1-1.lua Piecewise1.lua ~/LATEX/")
% (find-sh0 "cd ~/LUA/; cp -v Pict2e1.lua Pict2e1-1.lua Pict3D1.lua ~/LATEX/")
% (find-CN-aula-links "2022-1-C2-formulas-defs" "2" "c2m221fd" "c2fd")
% «.defs» (to "defs")
% «.title» (to "title")
% «.eqnp» (to "eqnp")
% «.RC» (to "RC")
% «.DefDif» (to "DefDif")
% «.TFC2» (to "TFC2")
% «.DFI» (to "DFI")
% «.MV» (to "MV")
% «.MV1-and-MV2» (to "MV1-and-MV2")
% «.MV-bases» (to "MV-bases")
% «.MVs» (to "MVs")
% «defs» (to ".defs")
\def\ph{\phantom}
\def\veq{\rotatebox{90}{$=$}}
% Difference with mathstrut
\def\Difms #1#2#3{\left. \mathstrut #3 \right|_{s=#1}^{s=#2}}
\def\Difmu #1#2#3{\left. \mathstrut #3 \right|_{u=#1}^{u=#2}}
\def\Difmx #1#2#3{\left. \mathstrut #3 \right|_{x=#1}^{x=#2}}
\def\Difmth#1#2#3{\left. \mathstrut #3 \right|_{θ=#1}^{θ=#2}}
% _____ _ _ _
% |_ _(_) |_| | ___ _ __ __ _ __ _ ___
% | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
% | | | | |_| | __/ | |_) | (_| | (_| | __/
% |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
% |_| |___/
%
% «title» (to ".title")
% (c2m221ftp 1 "title")
% (c2m221fda "title")
% (c2m221fta "title")
%
% Este arquivo só tem definições!
% Os testes estão num outro.
% «eqnp» (to ".eqnp")
\def\eqnpfull#1{\overset{\scriptscriptstyle(#1)}{=}}
\def\eqnpbare#1{=}
\def\eqnp{\eqnpbare}
% «RC» (to ".RC")
% (c2m221ftp 2 "RC")
% (c2m221fta "RC")
% (c2m221fda "RC")
\sa{[RC]}{\ensuremath{[\text{RC}]}}
\sa {RC} { \D \ddx f(g(x)) = f'(g(x))g'(x) }
\sa{(RC)}{\left( \D \ddx f(g(x)) \; = \; f'(g(x))g'(x) \right) }
% «DefDif» (to ".DefDif")
% (c2m221ftp 2 "DefDif")
% (c2m221fta "DefDif")
% (c2m221fda "DefDif")
\sa{[DefDif]}{\ensuremath{[\text{DefDif}]}}
\sa {DefDif} { \difx{a}{b}{F(x)} = F(b) - F(a) }
\sa{(DefDif)}{\left( \difx{a}{b}{F(x)} \; = \; F(b) - F(a) \right) }
% «TFC2» (to ".TFC2")
% (c2m221ftp 1 "TFC2")
% (c2m221fta "TFC2")
% (c2m221fda "TFC2")
\sa{[TFC2]} {\ensuremath{[\text{TFC2}]}}
\sa {TFC2} { \D \Intx{a}{b}{F'(x)} = \difx{a}{b}{F(x)} }
\sa{(TFC2)} {\left( \D \Intx{a}{b}{F'(x)} \; = \; \difx{a}{b}{F(x)} \right)}
% «DFI» (to ".DFI")
% (c2m221ftp 3 "DFI")
% (c2m221fta "DFI")
% (c2m221fda "DFI")
% (find-angg "LUA/C2Formulas1.lua" "DFI")
\sa{[DFI]}{\ensuremath{[\text{DFI}]}}
\sa {DFI} {
\begin{array}{lrcl}
\text{Se:} & f(g(x)) &\eqnp{1}& x \\
\text{Então:} & \ddx f(g(x)) &\eqnp{2}& \ddx x \\
&&\eqnp{3}& 1 \\
& \ddx f(g(x)) &\eqnp{4}& f'(g(x))g'(x) \\
& f'(g(x))g'(x) &\eqnp{5}& 1 \\
& g'(x) &\eqnp{6}& \D \frac{1}{f'(g(x))} \\
\end{array}}
\sa{(DFI)}{\left( \ga{DFI} \right)}
\sa{[DFI-]}{\ensuremath{[\text{DFI}^-]}}
\sa {DFI-} {
\begin{array}{lrcl}
\text{Se:} & f(g(x)) &\eqnp{1}& x \\
\text{Então:} & g'(x) &\eqnp{6}& \D \frac{1}{f'(g(x))} \\
\end{array}}
\sa{(DFI-)}{\left( \ga{DFI-} \right)}
% «MV» (to ".MV")
% (c2m221ftp 4 "MV")
% (c2m221fta "MV")
% (c2m221fda "MV")
\sa{[MV1]}{\ensuremath{[\text{MV}_1]}}
\sa{[MV2]}{\ensuremath{[\text{MV}_2]}}
\sa{[MV3]}{\ensuremath{[\text{MV}_3]}}
\sa{[MV4]}{\ensuremath{[\text{MV}_4]}}
\sa{(MV1)}{\left( \ga{MV1} \right)}
\sa{(MV2)}{\left( \ga{MV2} \right)}
\sa{(MV3)}{\left( \ga{MV3} \right)}
\sa{(MV4)}{\left( \ga{MV4} \right)}
\sa{[MVI1]}{\ensuremath{[\text{MVI}_1]}}
\sa{[MVI2]}{\ensuremath{[\text{MVI}_2]}}
\sa{[MVI3]}{\ensuremath{[\text{MVI}_3]}}
\sa{[MVI4]}{\ensuremath{[\text{MVI}_4]}}
\sa{(MVI1)}{\left( \ga{MVI1} \right)}
\sa{(MVI2)}{\left( \ga{MVI2} \right)}
\sa{(MVI3)}{\left( \ga{MVI3} \right)}
\sa{(MVI4)}{\left( \ga{MVI4} \right)}
% «MV1-and-MV2» (to ".MV1-and-MV2")
% (c2m221atisp 16 "um-exemplo")
% (c2m221atisa "um-exemplo")
\sa {MV1} {
\begin{array}{rcl}
\D \Intx{ a }{ b }{f'(g(x))g'(x)}
&\eqnp{1}& \D \difx{ a }{ b }{f (g(x)) } \\
&\eqnp{2}& f(g(b)) - f (g(a)) \\[7.5pt]
&\eqnp{3}& \D \difu{g(a)}{g(b)}{f (u)} \\[7.5pt]
&\eqnp{4}& \D \Intu{g(a)}{g(b)}{f'(u)}
\end{array}}
\sa {MV2} {
\begin{array}{rcl}
\D \Intx{ a }{ b }{f'(g(x))g'(x)}
%&\eqnp{1}& \D \difx{ a }{ b }{f (g(x)) } \\
%&\eqnp{2}& f(g(b)) - f (g(a)) \\[7.5pt]
%&\eqnp{3}& \D \difu{g(a)}{g(b)}{f (u)} \\[7.5pt]
&\eqnp{4}& \D \Intu{g(a)}{g(b)}{f'(u)}
\end{array}}
% (c2m221atisa "defs")
% (c2m221atisa "defs" "isubstbox")
% «MV-bases» (to ".MV-bases")
% (c2m221ftp 4 "MV-bases")
% (c2m221fta "MV-bases")
% (c2m221fda "MV-bases")
\sa{(MV base)}{ \left( \ga{MV base} \right) }
\sa {MV base} {
\begin{array}{rcl}
\multicolumn{3}{l}{\text{Se $\ga{MV hip}$ então:}} \\%[5pt]
\D \ga{MV nw} &=& \D \ga{MV ne} \\
\ga{MV veq} \\
\D \ga{MV sw} &=& \D \ga{MV se} \\
%\multicolumn{3}{l}{\text{Obs: $\ga{MV obs}$}} \\
\end{array}
}
\sa{(MVI base)}{ \left( \ga{MVI base} \right) }
\sa {MVI base} {
\begin{array}{rcl}
\multicolumn{3}{l}{\text{Se $\ga{MV hip}$ então:}} \\%[5pt]
\D \ga{MV nw} &=& \D \ga{MV ne} \\
\ga{MV veq} \\
\D \ga{MV sw} &=& \D \ga{MV se} \\
\multicolumn{3}{l}{\text{Obs: $\ga{MV obs}$}} \\
\end{array}
}
\sa{(MV- base)}{ \left( \ga{MV- base} \right) }
\sa {MV- base} {
\begin{array}{l}
\D \ga{MV ne} \\
\ga{MV veq} \\
\D \ga{MV se} \\
\end{array}
}
\sa{(MVI- base)}{ \left( \ga{MVI- base} \right) }
\sa {MVI- base} {
\begin{array}{c}
\D \ga{MV ne} \\
\ga{MV veq} \\
\D \ga{MV se} \\
\text{Obs: $\ga{MV obs}$} \\
\end{array}
}
\sa{MV hip}{hip}
\sa{MV nw}{nw}
\sa{MV ne}{ne}
\sa{MV veq}{\veq}
\sa{MV sw}{sw}
\sa{MV se}{se}
\sa{MV obs}{obs}
% «MVs» (to ".MVs")
% (c2m221ftp 5 "MVs")
% (c2m221fta "MVs")
% (c2m221fda "MVs")
% (find-angg "LUA/C2Formulas1.lua" "MVs")
% (c2m221atisp 22 "subst-int-def")
% (c2m221atisa "subst-int-def")
\sa{(MV3)}{ \left( \ga{MV3} \right) }
\sa {MV3} {{
\sa{MV hip} {F'(u) = f(u)}
\sa{MV ne} {\Intx{a}{b}{f(g(x))g'(x)}}
\sa{MV nw} {\Difmx{a}{b}{F(g(x))}}
\sa{MV veq} {\veq \ph{mm}}
\sa{MV sw} {\Difmu{g(a)}{g(b)}{F(u)}}
\sa{MV se} {\Intu{g(a)}{g(b)}{f(u)}}
\ga{MV base}
}}
\sa{(MVI3)}{ \left( \ga{MVI3} \right) }
\sa {MVI3} {{
\sa{MV hip} {F'(u) = f(u)}
\sa{MV ne} {\intx{f(g(x))g'(x)}}
\sa{MV nw} {F(g(x))}
\sa{MV veq} {\veq \ph{mm}}
\sa{MV sw} {F(u)}
\sa{MV se} {\intu{f(u)}}
\sa{MV obs} {u = g(x)}
\ga{MVI base}
}}
\sa{(MV4)}{ \left( \ga{MV4} \right) }
\sa {MV4} {{
\sa{MV ne} {\Intx{a}{b}{f(g(x))g'(x)}}
\sa{MV veq} {\ph{mmmm} \veq}
\sa{MV se} {\Intu{g(a)}{g(b)}{f(u)}}
\ga{MV- base}
}}
\sa{(MVI4)}{ \left( \ga{MVI4} \right) }
\sa {MVI4} {{
\sa{MV ne} {\intx{f(g(x))g'(x)}}
\sa{MV veq} {\veq}
\sa{MV se} {\intu{f(u)}}
\sa{MV obs} {u = g(x)}
\ga{MVI- base}
}}
% (c2m221atisp 30 "S3I")
% (c2m221atisa "S3I")
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2fd"
% ee-tla: "c2m221fd"
% End: