\documentclass[10pt,a4paper]{article}

% Packages
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\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{gabiisr}
\pdfinfo{
  /Title (calculo-i.pdf)
  /Creator (Cheatography)
  /Author (gabiisr)
  /Subject (Cálculo I Cheat Sheet)
}

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% Commands
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% Header and Footer
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\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Cálculo I Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{gabiisr} via \textcolor{DarkBackground}{\uline{cheatography.com/148135/cs/32278/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}gabiisr \\
  \uline{cheatography.com/gabiisr} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 5th June, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{4.4793 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Limites Fundamentais}}  \tn
% Row 0
\SetRowColor{LightBackground}
lim   c\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & c \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
lim   x\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & a \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.92234 cm} x{0.82386 cm} x{1.8308 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Limites Notáveis}}  \tn
% Row 0
\SetRowColor{LightBackground}
lim   1/x\textasciicircum{}n\textasciicircum{}\{\{nl\}\}\textasciicircum{}∆x→±∞\textasciicircum{} & 0 & n ∈ ℚ \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
lim   1/x\textasciicircum{}n\textasciicircum{}\{\{nl\}\}\textasciicircum{}∆x→0+\textasciicircum{} & +∞ &  \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
lim   1/x\textasciicircum{}n\textasciicircum{}\{\{nl\}\}\textasciicircum{}∆x→0-\textasciicircum{} & +∞\{\{nl\}\}-∞ & se n é par\{\{nl\}\}se n é ímpar \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{lim   f(x)\{\{nl\}\}\textasciicircum{}∆x→0\textasciicircum{}} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.73926 cm} x{2.38004 cm} p{0.4577 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Derivadas: Propriedades}}  \tn
% Row 0
\SetRowColor{LightBackground}
h(x) = f(x) + g(x)\{\{nobreak\}\} & h'(x) = f'(x) + g'(x) &  \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
h(x) = f(x) . g(x) & h'(x) = f'(x) . g(x) + f(x)  . g'(x) &  \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
h(x) = f(x) / g(x) \{\{nobreak\}\} & h'(x) = {[} f'(x) . g(x) - f(x)  . g'(x) {]} / {[} g(x) {]}\textasciicircum{}2\textasciicircum{} \{\{nobreak\}\} &  \tn 
% Row Count 8 (+ 4)
% Row 3
\SetRowColor{white}
h(x) = x\textasciicircum{}α\textasciicircum{} & h'(x) = α . x\textasciicircum{}α - 1\textasciicircum{} & α ∈ Q \tn 
% Row Count 10 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{δ e ε}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/gabiisr_1654448140_Untitled presentation (1).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{para todo ε \textless{} 0, existe um δ \textless{} 0, tal que se \newline 0 \textless{} | x - a| \textless{}δ então | f(x) - L| \textless{} ε .}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{δ e ε}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/gabiisr_1654448167_Untitled presentation (1).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{para todo ε \textless{} 0, existe um δ \textless{} 0, tal que se \newline 0 \textless{} | x - a| \textless{}δ então | f(x) - L| \textless{} ε .}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Derivada da Função no Ponto x1}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/gabiisr_1654039711_CodeCogsEqn (41).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Definição da Derivada}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/gabiisr_1654039459_CodeCogsEqn (40).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{É o operador que realiza o limite de uma função em x, quando Δx tende a 0.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Derivadas Notáveis}}  \tn
% Row 0
\SetRowColor{LightBackground}
d/dx log  ~   x \{\{nl\}\}  ~  ~ ~ ~ ~ ~ ~    \textasciicircum{}a\textasciicircum{} & (log ~  e )/ x \{\{nl\}\}~~  ~ ~ \textasciicircum{}a\textasciicircum{} \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
d /dx  a\textasciicircum{}x\textasciicircum{} & a \textasciicircum{}x\textasciicircum{} {\emph{ln}} (a) \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.55618 cm} x{1.51041 cm} x{1.51041 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Limites: Propriedades}}  \tn
% Row 0
\SetRowColor{LightBackground}
lim f(x) + g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & \{\{nobreak\}\}lim f(x) + lim g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{}   ~~~~~  \textasciicircum{}∆x→a\textasciicircum{} &  \tn 
% Row Count 7 (+ 7)
% Row 1
\SetRowColor{white}
lim f(x) . g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & lim f(x) . lim g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{}   ~~~~  \textasciicircum{}∆x→a\textasciicircum{} &  \tn 
% Row Count 13 (+ 6)
% Row 2
\SetRowColor{LightBackground}
lim f(x) / g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & \{\{nobreak\}\}lim f(x) / lim g(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{}   ~~~~  \textasciicircum{}∆x→a\textasciicircum{} & se lim g(x) ≠ 0\{\{nl\}\}~~~~\textasciicircum{}∆x→a\textasciicircum{} \tn 
% Row Count 20 (+ 7)
% Row 3
\SetRowColor{white}
lim c . f(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & c . lim f(x)\{\{nl\}\}~~~~\textasciicircum{}∆x→a\textasciicircum{} &  \tn 
% Row Count 24 (+ 4)
% Row 4
\SetRowColor{LightBackground}
\{\{nobreak\}\}lim {[} f(x) {]}\textasciicircum{}n\textasciicircum{}\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & \{\{nobreak\}\}{[} lim f(x) {]}\textasciicircum{}n\textasciicircum{}\{\{nl\}\}~\textasciicircum{}∆x→a\textasciicircum{} & \{\{nobreak\}\}para n \textless{} 0 * \{\{nl\}\}se lim f(x) ≥ 0, n ∈ Z pares \{\{nl\}\}se lim f(x) ≤ 0, n ∈ Z ímpares \tn 
% Row Count 32 (+ 8)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{1.55618 cm} x{1.51041 cm} x{1.51041 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Limites: Propriedades (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
\{\{nobreak\}\}lim ~ log f(x)\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{}~~~~ \textasciicircum{}b\textasciicircum{} & \{\{nobreak\}\}log ~~ . {[} lim f(x) {]} \{\{nl\}\}~~~~~\textasciicircum{}b\textasciicircum{}~~~\textasciicircum{} ∆x→a\textasciicircum{} & se lim f(x) \textgreater{} 0 \tn 
% Row Count 9 (+ 9)
% Row 6
\SetRowColor{white}
\{\{nobreak\}\}lim ~cos( f(x) )\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & cos( lim f(x) )\{\{nl\}\} ~~~~~~~\textasciicircum{}∆x→a\textasciicircum{} & para sen eoutras funções \seqsplit{trigonométricas} \tn 
% Row Count 15 (+ 6)
% Row 7
\SetRowColor{LightBackground}
\{\{nobreak\}\}lim ~~e\textasciicircum{}f(x)\textasciicircum{}\{\{nl\}\}\textasciicircum{}∆x→a\textasciicircum{} & \{\{nobreak\}\}e\textasciicircum{} lim f(x)\textasciicircum{} &  \tn 
% Row Count 19 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}