% (find-angg "LATEX/2018-2-C2-P1fake.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2018-2-C2-P1fake.tex" :end))
% (defun d () (interactive) (find-xpdfpage "~/LATEX/2018-2-C2-P1fake.pdf"))
% (defun e () (interactive) (find-LATEX "2018-2-C2-P1fake.tex"))
% (defun u () (interactive) (find-latex-upload-links "2018-2-C2-P1fake"))
% (find-xpdfpage "~/LATEX/2018-2-C2-P1fake.pdf")
% (find-sh0 "cp -v  ~/LATEX/2018-2-C2-P1fake.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2018-2-C2-P1fake.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2018-2-C2-P1fake.pdf
%               file:///tmp/2018-2-C2-P1fake.pdf
%           file:///tmp/pen/2018-2-C2-P1fake.pdf
% http://angg.twu.net/LATEX/2018-2-C2-P1fake.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
\catcode`\^^J=10                      % (find-es "luatex" "spurious-omega")
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")
\def\expr#1{\directlua{output(tostring(#1))}}
\def\eval#1{\directlua{#1}}
%
\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



{\setlength{\parindent}{0em}
\footnotesize
\par Cálculo 2
\par PURO-UFF - 2018.2
\par P1 fake (treino pra P1) - 07/nov/2018 - 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

% (c2q)

1) \T(Total: 2.0 pts) Calcule $$\intx {(\sen x)^4}.$$

\bsk

2) \T(Total: 2.0 pts) Calcule $$\intx {\frac{1}{\sqrt{4-9x^2}}}.$$

\bsk

3) \T(Total: 2.0 pts) Calcule $$\intx {\frac{x^3}{x^2 + 4x - 12}}.$$

\bsk

4) \T(Total: 2.0 pts) Calcule $$\intx {\frac{x^3+1}{(x-4)^2}}.$$

\bsk

5) \T(Total: 2.0 pts) Calcule por integração por partes:

a) \B(1.0 pts) $\intx {e^{2x}\cos(3x)}$,

b) \B(1.0 pts) $\intx {xe^{2x}\cos(3x)}$.


\bsk
\bsk

Algumas definições, fórmulas e substituições:

$\begin{array}[t]{l}
 c = \cos θ \\
 s = \sen θ \\
 t = \tan θ \\
 z = \sec θ \\
 E = e^{iθ} \\
 \end{array}
 %
 \begin{array}[t]{l}
 c^2+s^2=1 \\
 z^2=t^2+1 \\
 \sqrt{1-s^2} = c \\
 \sqrt{1-t^2} = z \\
 \sqrt{z^2-1} = t \\
 \end{array}
 %
 \begin{array}[t]{l}
 \frac{ds}{dθ} = c \\
 \frac{dc}{dθ} = -s \\
 \frac{dt}{dθ} = z^2 \\
 \frac{dz}{dθ} = zt \\
 \end{array}
 %
 \begin{array}[t]{l}
 E = c+is \\
 c = \frac{E+E¹}{2} \\
 s = \frac{E-E¹}{2i} \\
 e^{ikθ} + e^{-ikθ} = 2 \cos kθ \\
 e^{ikθ} - e^{-ikθ} = 2i \sen kθ \\
 \end{array}
$





\end{document}

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