% (find-LATEX "2024-2-C2-teste-niv.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2024-2-C2-teste-niv.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2024-2-C2-teste-niv.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2024-2-C2-teste-niv.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2024-2-C2-teste-niv.pdf"))
% (defun e () (interactive) (find-LATEX "2024-2-C2-teste-niv.tex"))
% (defun o () (interactive) (find-LATEX "2024-1-C2-teste-niv.tex"))
% (defun u () (interactive) (find-latex-upload-links "2024-2-C2-teste-niv"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2024-2-C2-teste-niv.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2024-2-C2-teste-niv")
% (find-pdf-page   "~/LATEX/2024-2-C2-teste-niv.pdf")
% (find-sh0 "cp -v  ~/LATEX/2024-2-C2-teste-niv.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2024-2-C2-teste-niv.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2024-2-C2-teste-niv.pdf")
%   file:///home/edrx/LATEX/2024-2-C2-teste-niv.pdf
%               file:///tmp/2024-2-C2-teste-niv.pdf
%           file:///tmp/pen/2024-2-C2-teste-niv.pdf
%  http://anggtwu.net/LATEX/2024-2-C2-teste-niv.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps   "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2024-2-C2-teste-niv" "2" "c2m242tn" "c2tn")

% «.defs»		(to "defs")
% «.defs-T-and-B»	(to "defs-T-and-B")
% «.defs-caepro»	(to "defs-caepro")
% «.defs-pict2e»	(to "defs-pict2e")
% «.defs-maxima»	(to "defs-maxima")
% «.defs-V»		(to "defs-V")
% «.title»		(to "title")
% «.links»		(to "links")



\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-LATEX "dednat7-test1.tex")
%\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")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

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

\def\drafturl{http://anggtwu.net/LATEX/2024-2-C2.pdf}
\def\drafturl{http://anggtwu.net/2024.2-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2024-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2024-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat7load.lua"}  % (find-LATEX "dednat7load.lua")
\directlua{dednat7preamble()}         % (find-angg "LUA/DednatPreamble1.lua")
\directlua{dednat7oldheads()}         % (find-angg "LUA/Dednat7oldheads.lua")

% «defs-T-and-B»  (to ".defs-T-and-B")
\long\def\ColorDarkOrange#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){\ColorDarkOrange{\bf(#1 pts)}}

% «defs-caepro»  (to ".defs-caepro")
%L dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L dofile "Piecewise2.lua"           -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua"           -- (find-LATEX "Escadas1.lua")
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt

% «defs-maxima»  (to ".defs-maxima")
%L dofile "Maxima2.lua"              -- (find-angg "LUA/Maxima2.lua")
\pu

% «defs-V»  (to ".defs-V")
%L --- See: (find-angg "LUA/MiniV1.lua" "problem-with-V")
%L V = MiniV
%L v = V.fromab
\pu


%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m242tnp 1 "title")
% (c2m242tna   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 2 - 2024.2}

\bsk

Aula 4: teste de nivelamento

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://anggtwu.net/2024.2-C2.html}

\end{center}

\newpage

% «links»  (to ".links")
% (c2m242tnp 2 "links")
% (c2m242tna   "links")

{\bf Links}

\scalebox{0.6}{\def\colwidth{16cm}\firstcol{

% (find-books "__analysis/__analysis.el" "stewart-pt" "138" "Diga o que são f e a")
\par \Ca{StewPtCap2p67} (p.138) Exercícios 33--38: ...diga o que são $f$ e $a$.

}\anothercol{
}}

\newpage

% (find-books "__analysis/__analysis.el" "stewart-pt" "138" "Diga o que são f e a")
% (find-stewart71ptpage (+ 27 138) "33-38 ... Diga o que são f e a")
\sa{33}{\lim_{h \to 0}  \frac {(1+h)^{10} - 1}   {h}}
\sa{34}{\lim_{h \to 0}  \frac {\sqrt[4]{16+h}-2} {h}}
\sa{35}{\lim_{x \to 5}  \frac {2^x - 32}         {x-5}}
\sa{36}{\lim_{x \to π/4}\frac {\tan x - 1}       {x-π/4}}   % difícil
\sa{37}{\lim_{h \to 0}  \frac {\cos(π+h) + 1}    {h}}
\sa{38}{\lim_{t \to 1}  \frac {t^4+t-2}          {t-1}}

\def\P#1{\left( #1 \right)}
\sa{D1}{f'(x) \;=\; \lim_{ε \to 0} \frac {f(x+ε)-f(x)} {ε}}
\sa{D2}{f'(a) \;=\; \lim_{ε \to 0} \frac {f(a+ε)-f(a)} {ε}}
\sa{D3}{f'(a) \;=\; \lim_{x \to a} \frac {f(x)-f(a)} {x-a}}
\sa{(D1)}{\P{\ga{D1}}}
\sa{(D2)}{\P{\ga{D2}}}
\sa{(D3)}{\P{\ga{D3}}}
\sa{[D1]}{\CFname{D1}{}}
\sa{[D2]}{\CFname{D2}{}}
\sa{[D3]}{\CFname{D3}{}}




% {\bf Por favor escrevam...}

\scalebox{0.5}{\def\colwidth{9.5cm}\firstcol{

{}

{\sl Este teste é só pra eu descobrir o quanto vocês sabem de certas
  técnicas de Cálculo 1 -- eu vou usar as informações daqui pra
  decidir como organizar o curso.}

\msk

Por favor escrevam:

\begin{itemize}

\item seu nome legível (em todas as folhas),

\item com quem você fez GA, C1 e Prog1 no semestre em que você passou
  em cada uma, e em qual semestre foi,

\item as respostas dos exercícios à direita e tudo que você conseguir
  fazer pra tentar resolver eles.

\end{itemize}

Dicas (que você não é obrigado a usar!):

$$\ga{D1}$$
$$\ga{D2}$$
$$\ga{D3}$$
$$f'(a) \;=\; \left. \P{\ddx f(x)} \right|_{x=a}$$

Obs: eu tirei os exercícios à direita do Stewart: % Links:

\par \ssk
\par \Ca{StewPtCap2p62} (p.133) Definição da derivada
\par \Ca{StewPtCap2p67} (p.138) Exercícios 33--38


}\def\colwidth{5cm}\anothercol{

{}

Cada limite abaixo representa a derivada de certa função $f$ em certo
número $a$. Diga o que são $f$ e $a$ em cada caso.

\bsk

\def\myline#1#2{#1) & $\D\ga{#2}$ \\\\[-8pt]}
 \begin{tabular}{ll}
 \myline{a}{33}
 \myline{b}{34}
 \myline{c}{35}
 \myline{d}{37}
 \myline{d}{38}
 \end{tabular}


}}


\newpage

% Basic configurables:
\sa{DD-reset}{
  \sa{x}{x}
  \sa{a}{a}
  \sa{e}{ε}
  \sa{f(farg)}{f(\ga{farg})}
  }
\ga{DD-reset}

\def\setaxef#1#2#3#4{
  \sa{a}{#1}
  \sa{x}{#2}
  \sa{e}{#3}
  \sa{f(farg)}{#4}
  }
%\setaxef {a} {x} {ε} {f(\ga{farg})}

% Trivials:
\def\fof#1{\sa{farg}{#1}
           \ga{f(farg)}}

\sa      {a+e}           {\ga{a}+\ga{e}}
\sa      {x+e}           {\ga{a}+\ga{e}}
\sa    {f(a+e)}          {\fof{\ga{a}+\ga{e}}}
\sa    {f(x+e)}          {\fof{\ga{x}+\ga{e}}}
\sa           {f(x)}     {\fof{\ga{x}}}
\sa           {f(a)}     {\fof{\ga{a}}}
\sa    {f(x+e)-f(x)}     {\ga{f(x+e)}-\ga{f(x)}}
\sa    {f(a+e)-f(a)}     {\ga{f(a+e)}-\ga{f(a)}}
\sa    {f(x+e)-f(x)/e}   {\frac{\ga{f(x+e)-f(x)}}{\ga{e}}}
\sa    {f(a+e)-f(a)/e}   {\frac{\ga{f(a+e)-f(a)}}{\ga{e}}}
\sa{lim f(x+e)-f(x)/e}   {\lim_{\ga{e}\to0} \ga{f(x+e)-f(x)/e}}
\sa{lim f(a+e)-f(a)/e}   {\lim_{\ga{e}\to0} \ga{f(a+e)-f(a)/e}}

\sa    {f(x)}            {\fof{\ga{x}}}
\sa         {f(a)}       {\fof{\ga{a}}}
\sa    {f(x)-f(a)}       {\ga{f(x)}-\ga{f(a)}}
\sa              {x-a}   {\ga{x}-\ga{a}}
\sa    {f(x)-f(a)/x-a}   {\frac{\ga{f(x)}-\ga{f(a)}}{\ga{x-a}}}
\sa{lim f(x)-f(a)/x-a}   {\lim_{\ga{x}\to\ga{a}} \ga{f(x)-f(a)/x-a}}

\sa {ddx f(x)}           {\frac{d}{d\ga{x}} \ga{f(x)}}
\sa{(ddx f(x))|x=a}      {\left.\left( \ga{ddx f(x)} \right)\right|_{\ga{x}=\ga{a}}}

\sa{(ddx f(x))|x=a = lim f(x+e)-f(x)/e}
                         {\ga{(ddx f(x))|x=a} \;=\; \ga{lim f(x+e)-f(x)/e}}
\sa{(ddx f(x))|x=a = lim f(a+e)-f(a)/e}
                         {\ga{(ddx f(x))|x=a} \;=\; \ga{lim f(a+e)-f(a)/e}}
\sa{(ddx f(x))|x=a = lim f(x)-f(a)/x-a}
                         {\ga{(ddx f(x))|x=a} \;=\; \ga{lim f(x)-f(a)/x-a}}

\sa{DDxa}{\ga{(ddx f(x))|x=a = lim f(x)-f(a)/x-a}}
\sa{DDae}{\ga{(ddx f(x))|x=a = lim f(a+e)-f(a)/e}}
\sa{DDxe}{\ga{(ddx f(x))|x=a = lim f(x+e)-f(x)/e}}
\sa {Lae}                 {\ga{lim f(a+e)-f(a)/e}}
\sa {Lxa}                 {\ga{lim f(x)-f(a)/x-a}}
\sa {Lxe}                 {\ga{lim f(x+e)-f(x)/e}}
\sa {Qae}                     {\ga{f(a+e)-f(a)/e}}
\sa {Qxa}                     {\ga{f(x)-f(a)/x-a}}
\sa {Qxe}                     {\ga{f(x+e)-f(x)/e}}

\sa{(DDae)}{\P{\ga{DDae}}}
\sa{(DDxa)}{\P{\ga{DDxa}}}
\sa{(DDxe)}{\P{\ga{DDxe}}}
\sa {(Lae)}{\P{\ga{Lae}}}
\sa {(Lxa)}{\P{\ga{Lxa}}}
\sa {(Lxe)}{\P{\ga{Lxe}}}
\sa {(Qae)}{\P{\ga{Qae}}}
\sa {(Qxa)}{\P{\ga{Qxa}}}
\sa {(Qxe)}{\P{\ga{Qxe}}}

\sa{[DDxa]}{\CFname{DD}{xa}}
\sa{[DDxe]}{\CFname{DD}{xε}}
\sa{[DDae]}{\CFname{DD}{aε}}
\sa{[Lxa]}{\CFname{L}{xa}}
\sa{[Lxe]}{\CFname{L}{xε}}
\sa{[Lae]}{\CFname{L}{aε}}
\sa{[Qxa]}{\CFname{Q}{xa}}
\sa{[Qxe]}{\CFname{Q}{xε}}
\sa{[Qae]}{\CFname{Q}{aε}}

\scalebox{0.5}{\def\colwidth{10.5cm}\firstcol{

\vspace*{0cm}

$\begin{array}{lcr}
  \ga{[DDae]} &=& \D \ga{(DDae)} \\\\[-11pt]
  \ga{[DDxe]} &=& \D \ga{(DDxe)} \\\\[-11pt]
  \ga{[DDxa]} &=& \D \ga{(DDxa)} \\\\[-4pt]
  \ga{[Lae]}  &=& \D \ga{(Lae)}  \\\\[-11pt]
  \ga{[Lxe]}  &=& \D \ga{(Lxe)}  \\\\[-11pt]
  \ga{[Lxa]}  &=& \D \ga{(Lxa)}  \\\\[-4pt]
  \ga{[Qae]}  &=& \D \ga{(Qae)}  \\\\[-11pt]
  \ga{[Qxe]}  &=& \D \ga{(Qxe)}  \\\\[-11pt]
  \ga{[Qxa]}  &=& \D \ga{(Qxa)}  \\
  \end{array}
$

}\def\colwidth{14cm}\anothercol{

% \def\setaxef#1#2#3#4{
%   \sa{e}{#1}
%   \sa{x}{#2}
%   \sa{a}{#3}
%   \sa{f(farg)}{#3}
%   }
% 
% % \setaxef {a} {x} {ε} {f(\ga{farg})}
% %$\ga{[Qae]}  = \D \ga{(Qae)}$
% 
% \sa{x}{x}
% \sa{a}{a}
% \sa{e}{h}
% \sa{f(farg)}{f(\ga{farg})}

\vspace*{0cm}

$\ga{[Qae]}
  \bmat{ε:=\ga{e}}
  = \D \ga{(Qae)}
$

\sa{f(farg)}{(\ga{farg})^{10}}
$\ga{[Qae]} 
  \bmat{ε:=\ga{e} \\ f(x):=\fof{x}}
  = \D \ga{(Qae)}
$

\sa{a}{1}
$\ga{[Qae]}
  \bmat{ε:=\ga{e} \\ f(x):=\fof{x} \\ a:=\ga{a}}
  = \D \ga{(Qae)}
$


$\ga{[DDae]}
  \bmat{ε:=\ga{e} \\
        f(x):=\fof{x} \\
        a:=\ga{a} \\
       }
  = \D \ga{(DDae)}
$

}}

\newpage









\sa{DD-test1}{
  \sa{e}{h}
  \sa{x}{20}
  \sa{a}{30}
  \sa{f(farg)}{(\ga{farg})^5}
  }








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

\end{document}

% (find-pdfpages2-links "~/LATEX/" "2024-2-C2-teste-niv")


% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2tn"
% ee-tla: "c2m242tn"
% End:
