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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (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")
% «.defs-teste» (to "defs-teste")
\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")
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\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
% «defs-teste» (to ".defs-teste")
% (c2m242tnp 3 "defs-teste")
% (c2m242tna "defs-teste")
% (find-es "maxima" "2024.2-C2-teste-niv")
% (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: