% (find-angg "LATEX/2017-1-C2-VS.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2017-1-C2-VS.tex" :end))
% (defun d () (interactive) (find-xpdfpage "~/LATEX/2017-1-C2-VS.pdf"))
% (defun e () (interactive) (find-LATEX "2017-1-C2-VS.tex"))
% (defun u () (interactive) (find-latex-upload-links "2017-1-C2-VS"))
% (find-xpdfpage "~/LATEX/2017-1-C2-VS.pdf")
% (find-sh0 "cp -v  ~/LATEX/2017-1-C2-VS.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2017-1-C2-VS.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2017-1-C2-VS.pdf
%               file:///tmp/2017-1-C2-VS.pdf
%           file:///tmp/pen/2017-1-C2-VS.pdf
% http://angg.twu.net/LATEX/2017-1-C2-VS.pdf
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
%\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage{color}                % (find-LATEX "edrx15.sty" "colors")
\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{edrx15}               % (find-angg "LATEX/edrx15.sty")
\input edrxaccents.tex            % (find-angg "LATEX/edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-dn4ex "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
\begin{document}

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

\directlua{dofile "edrxtikz.lua"} % (find-LATEX "edrxtikz.lua")
\directlua{dofile "edrxpict.lua"} % (find-LATEX "edrxpict.lua")
%L V.__tostring = function (v) return format("(%.3f,%.3f)", v[1], v[2]) end




{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 2
\par PURO-UFF - 2017.1
\par VS - 19/jul/2017 - 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



% (find-angg "LATEX/2015-2-GA-P2.tex")

1) \T(Total: 1.0 pts) Calcule $$\Intx{a}{b}{x \sqrt{1-x^2}}.$$

2) \T(Total: 1.0 pts) Teste o resultado do item anterior.

\bsk

3) \T(Total: 2.0 pts) Calcule $$\intx {x \sen(ax+b)}.$$

4) \T(Total: 6.0 pts) Calcule $$\intx {\frac{x}{x^2+1}}.$$

% Dicas pro 4: você vai precisar de uma substituição trigonométrica e
% outras substituições.
% 
% a) \B(1.0 pts) Represente graficamente $r_0 = \setofst{P∈\R^2}{\Vec{AP}·\Vec{AB}=0}$.
% 
% b) \B(1.0 pts) Represente graficamente $r_2 = \setofst{P∈\R^2}{\Vec{AP}·\Vec{AB}=2}$.


\bsk
\bsk
\bsk

Dicas:
$\bsm{s=\senθ \\ \sqrt{1-s^2}=\cosθ   \\ ds=\cosθ\,dθ \\ θ=\arcsen s}$,
$\bsm{t=\tanθ \\ \sqrt{1+t^2}=\secθ=z \\ dt=  z^2\,dθ \\ θ=\arctan t}$,
$\bsm{z=\secθ \\ \sqrt{z^2-1}=\tanθ=t \\ dz=   zt\,dθ \\ θ=\arcsec z}$,



% Gabarito:
% (find-es "ipython" "2017.1-C2-VS")





\end{document}

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