% (find-angg "LATEX/2019-1-C3-P2.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2019-1-C3-P2.tex"))
% (defun d () (interactive) (find-pdf-page "~/LATEX/2019-1-C3-P2.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2019-1-C3-P2.pdf"))
% (defun b () (interactive) (find-zsh "bibtex 2019-1-C3-P2; makeindex 2019-1-C3-P2"))
% (defun e () (interactive) (find-LATEX "2019-1-C3-P2.tex"))
% (defun u () (interactive) (find-latex-upload-links "2019-1-C3-P2"))
% (find-xpdfpage "~/LATEX/2019-1-C3-P2.pdf")
% (find-sh0 "cp -v  ~/LATEX/2019-1-C3-P2.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2019-1-C3-P2.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2019-1-C3-P2.pdf
%               file:///tmp/2019-1-C3-P2.pdf
%           file:///tmp/pen/2019-1-C3-P2.pdf
% http://angg.twu.net/LATEX/2019-1-C3-P2.pdf
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
%\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{edrx15}               % (find-LATEX "edrx15.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-angg ".emacs.papers" "latexgeom")
% (find-LATEXfile "2016-2-GA-VR.tex" "{geometry}")
% (find-latexgeomtext "total={6.5in,8.75in},")
\usepackage[%paperwidth=11.5cm, paperheight=9cm,
            %total={6.5in,4in},
            %textwidth=4in,  paperwidth=4.5in,
            %textheight=5in, paperheight=4.5in,
            a4paper,
            top=3.5cm, bottom=3.5cm, left=4cm, right=4cm, includefoot
           ]{geometry}
%
\begin{document}

% \catcode`\^^J=10
% \directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")
% 
% %L dofile "edrxtikz.lua"  -- (find-LATEX "edrxtikz.lua")
% %L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
% \pu

\def\Fr {\mathsf{Fr}}
\def\Int{\mathsf{Int}}
\def\ovl{\overline}




{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 3
\par PURO-UFF - 2019.1
\par P2 - 4/julho/2019 - Eduardo Ochs
\par Respostas sem justificativas não serão aceitas.
\par Proibido usar quaisquer aparelhos eletrônicos.

}

\bsk
\bsk

\setlength{\parindent}{0em}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\B       (#1 pts){{\bf(#1 pts)}}
% Usage:
% 1) \T(Total: 2.34 pts) Foo
% a) \B(0.45 pts) Bar


% \bsk
% \bsk

% (c3qe)



1) \T(Total: 3.0 pts) Seja $F(x,y)=xy$ e sejam
%
$$\begin{array}{l}
 A=\setofxyst{0≤x, 0≤y, x+y<1}, \\
 B=\setofxyst{0≤x, 0≤y, x+y≤1}, \\
 C=\setofxyst{0≤x, 0≤y, 1≤x+y}. \\
 \end{array}
$$

a) \B(1.0 pts) Represente graficamente o conjunto $A$ e diga se dá pra
usar o teorema de Weierstrass pra garantir que $F$ tem um máximo e um
mínimo globais no conjunto $A$.

b) \B(1.0 pts) Idem, mas para o conjunto $B$.

c) \B(1.0 pts) Idem, mas para o conjunto $C$.



\bsk
\bsk

2) \T(Total: 2.0 pts) Seja $A = \{1,\frac12,\frac13,\frac14,\ldots\}$.

a) \B(0.6 pts) Represente graficamente $A$.

b) \B(0.8 pts) Explique porque $0∈\Fr(A)$.

c) \B(0.6 pts) Explique porque $A$ não é fechado.

\bsk
\bsk

(Ooops! Redigitar a questão 3...)

% Questão sobre polinômio de Taylor:
%   F(x,y) = 
% (find-LATEX "2019-2-C3-material.tex" "taylor-2D")

% \bsk
% \bsk
% 
% 1) Calcule $\frac{d}{dt} \frac{d}{dt} F(g(t),h(t))$.
% 
% 2) Calcule $\frac{d}{dt} \frac{d}{dt} F(g(t_0),h(t_0))$ no caso em que:
% 
% $\begin{array}{rcl}
%  t_0 &=& 6, \\
%  g(6) &=& 7, \\
%  h(6) &=& 8, \\
%  g'(6) &=& 1, \\
%  g''(t) &=& 0, \\
%  h''(t) &=& 0, \\
%  F(x,y) &=& a(x-7)^2 - b(x-7)(y-8) + c(y-8)^2. \\
%  \end{array}
% $




% (c3qe)
% (c3q191 27 "20190607" "Int")
% (c3q191 29 "20190627" "Int")



%\newpage

%{\bf Gabarito}

% (find-es "sympy" "lagrange-multipliers")




\end{document}

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