% (find-LATEX "2021-2-C3-VS.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2021-2-C3-VS.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2021-2-C3-VS.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2021-2-C3-VS.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2021-2-C3-VS.pdf"))
% (defun e () (interactive) (find-LATEX "2021-2-C3-VS.tex"))
% (defun o () (interactive) (find-LATEX "2021-2-C3-VS.tex"))
% (defun u () (interactive) (find-latex-upload-links "2021-2-C3-VS"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2021-2-C3-VS.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2021-2-C3-VS")
% (find-pdf-page   "~/LATEX/2021-2-C3-VS.pdf")
% (find-sh0 "cp -v  ~/LATEX/2021-2-C3-VS.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2021-2-C3-VS.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2021-2-C3-VS.pdf")
%   file:///home/edrx/LATEX/2021-2-C3-VS.pdf
%               file:///tmp/2021-2-C3-VS.pdf
%           file:///tmp/pen/2021-2-C3-VS.pdf
% http://angg.twu.net/LATEX/2021-2-C3-VS.pdf
% (find-LATEX "2019.mk")
% (find-CN-aula-links "2021-2-C3-VS" "3" "c3m212vs" "c3vs")

% «.defs»		(to "defs")
% «.defs-T-and-B»	(to "defs-T-and-B")
% «.title»		(to "title")
%
% «.djvuize»		(to "djvuize")



% <videos>
% Video (not yet):
% (find-ssr-links     "c3m212vs" "2021-2-C3-VS")
% (code-eevvideo      "c3m212vs" "2021-2-C3-VS")
% (code-eevlinksvideo "c3m212vs" "2021-2-C3-VS")
% (find-c3m212vsvideo "0:00")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%\usepackage{emaxima}              % (find-LATEX "emaxima.sty")
%
%\usepackage[backend=biber,
%   style=alphabetic]{biblatex}            % (find-es "tex" "biber")
%\addbibresource{catsem-slides.bib}        % (find-LATEX "catsem-slides.bib")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

%\catcode`\^^J=10
%\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")
%
% %L dofile "2021pict2e.lua"           -- (find-LATEX "2021pict2e.lua")
% %L Pict2e.__index.suffix = "%"
% \pu
% \def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
% \def\pictaxesstyle{\linethickness{0.5pt}}

% %L dofile "edrxtikz.lua"  -- (find-LATEX "edrxtikz.lua")
% %L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
% \pu

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\u#1{\par{\footnotesize \url{#1}}}

\def\drafturl{http://angg.twu.net/LATEX/2021-2-C3.pdf}
\def\drafturl{http://angg.twu.net/2021.2-C3.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}


% «defs-T-and-B»  (to ".defs-T-and-B")
% (c3m202p1p 6 "questao-2")
% (c3m202p1a   "questao-2")
\long\def\ColorOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B       (#1 pts){\ColorOrange{\bf(#1 pts)}}
%
% (defun T () (interactive) (insert "\\T(Total: ?.? pts)\n"))
% (defun B () (interactive) (insert "a) \\B(?.? pts)\n"))




%  _____ _ _   _                               
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%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c3m212vsp 1 "title")
% (c3m212vsa   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 3 - 2021.2}

\bsk

Prova final (VS)

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://angg.twu.net/2021.2-C3.html}

\end{center}

\newpage

As regras e dicas são as mesmas das provas e dos mini-testes,

mas a prova vai ser disponibilizada às 16:30 da sexta

11/fev/2021 e deve ser entregue até as 20:00 do sábado

12/fev/2021.

\bsk

Organize muito bem as suas respostas.

\bsk

Veja o PDFzão com todos os PDFzinhos do curso:

\ssk

{\footnotesize

\url{http://angg.twu.net/LATEX/2021-2-C3-tudo.pdf}

}


\newpage

\def\derivs{\mathsf{derivs}}

{\bf Questão 1.}

\T(Total: 3.0 pts)

\msk

Seja $f(x)=\ln x$.

\msk

a) \B(1.0 pts) Calcule $\derivs_1^2(f(x))$. 

b) \B(2.0 pts) Use isto pra calcular uma boa aproximação para $f(1.1)$.

\bsk

Faça todas as suas contas à mão.

Tem material sobre esse assunto aqui:

\ssk

{\footnotesize

% (c3tup 131)
%    http://angg.twu.net/LATEX/2021-2-C3-tudo.pdf#page=131
\url{http://angg.twu.net/LATEX/2021-2-C3-tudo.pdf#page=131}

}


\newpage

% (c3tup 71)
% (c3m212nfp 21 "derivadas-parciais-th")
% (c3m212nfa    "derivadas-parciais-th")
% (find-books "__analysis/__analysis.el" "thompson")
% (find-sthompsonpage (+ 11 172) "XVI. Partial Differentiation")
% (find-sthompsonpage (+ 11 178) "(5)")

{\bf Questão 2.}

\T(Total: 7.0 pts)

\msk

Faça o exercício (5) da página 178 do Thompson usando exatamente a
versão dele da ``notação de físicos'' e seguindo todas as convenções
notacionais dele. Faça as suas contas bem passo a passo.

Obs: ele define ``total differentials'' na página 173, e você pode
usar o ``useful dodge'' do capítulo IX dele (o ``truque das variáveis
novas'') se você achar que ajuda.

Você vai precisar fazer outros exercícios mais fáceis do Thompson pra
pegar o jeito. Inclua eles na sua resposta.

\bsk

\newpage

{\bf Questão 2: dicas}

\msk

Sugiro que você faça essa questão uma primeira vez no dia em que você
receber a prova e revise ela com muito cuidado várias vezes, umas no
mesmo dia e outras no dia seguinte... é comum idéias complicadas
ficarem mais fáceis quando a gente dorme.

\msk

Tem bastante material sobre notação de físicos aqui,

\ssk

{\footnotesize

% (c3tup 71)
%    http://angg.twu.net/LATEX/2021-2-C3-tudo.pdf#page=71
\url{http://angg.twu.net/LATEX/2021-2-C3-tudo.pdf#page=71}

}

\ssk

e tem muitas idéias importantes que estão nos vídeos e não estão nos
PDFs.




% Ideias:
% ALguns 
% (c3tup 33)
% (c3tup 38)
% (c3tup 47)
% (c3tup 61)
% (c3tup 69)
% (c3tup 71)
% (c3m212nfp 21 "derivadas-parciais-th")
% (c3m212nfa    "derivadas-parciais-th")
% (c3tup 92)
% (c3tup 101)
% (c3tup 106)
% (c3tup 129)
% (c3tup 132)




%\printbibliography

\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}

%  ____  _             _         
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% | | | | \ \ / / | | | |_  / _ \
% | |_| | |\ V /| |_| | |/ /  __/
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%     |__/                       
%
% «djvuize»  (to ".djvuize")
% (find-LATEXgrep "grep --color -nH --null -e djvuize 2020-1*.tex")

* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-fline "~/2021.2-C3/")
# (find-fline "~/LATEX/2021-2-C3/")
# (find-fline "~/bin/djvuize")

cd /tmp/
for i in *.jpg; do echo f $(basename $i .jpg); done

f () { rm -v $1.pdf;  textcleaner -f 50 -o  5 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf;  textcleaner -f 50 -o 10 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf;  textcleaner -f 50 -o 20 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }

f () { rm -fv $1.png $1.pdf; djvuize $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 15" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 30" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 45" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.5" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.25" $1.pdf; xpdf $1.pdf }
f () { cp -fv $1.png $1.pdf       ~/2021.2-C3/
       cp -fv        $1.pdf ~/LATEX/2021-2-C3/
       cat <<%%%
% (find-latexscan-links "C3" "$1")
%%%
}

f 20201213_area_em_funcao_de_theta
f 20201213_area_em_funcao_de_x
f 20201213_area_fatias_pizza



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%                        
% <make>

* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2021-2-C3-VS veryclean
make -f 2019.mk STEM=2021-2-C3-VS pdf

% Local Variables:
% coding: utf-8-unix
% ee-tla: "c3vs"
% ee-tla: "c3m212vs"
% End: