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\author{{[}deleted{]}}
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  /Title (qut-mxb100.pdf)
  /Creator (Cheatography)
  /Author ({[}deleted{]})
  /Subject (QUT MXB100 Cheat Sheet)
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{QUT MXB100 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{{[}deleted{]}} via \textcolor{DarkBackground}{\uline{cheatography.com/123338/cs/23171/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}{[}deleted{]} \\
  \uline{cheatography.com/deleted-123338} \\
  \end{tabulary}
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\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 11th June, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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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

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% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Differentiation}}  \tn
% Row 0
\SetRowColor{LightBackground}
gradient of a line & m = rise/run = (y2-y1)/(x2 -x1) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
as lim approaches 0 & m = (lim h→0) f(x + h) - f(x)/h \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
first derivative & f'(x) = df/dx \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
second derivative & f''(x) = d\textasciicircum{}2\textasciicircum{}f/dx\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
third derivative & f'''(x)=d\textasciicircum{}3\textasciicircum{}f/dx\textasciicircum{}3\textasciicircum{} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
d/dx x\textasciicircum{}n\textasciicircum{} = nx\textasciicircum{}n-1\textasciicircum{} & d/dx ln(x) - 1/x \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
d/dx e\textasciicircum{}x\textasciicircum{} = e\textasciicircum{}x\textasciicircum{} & d/dx sin(x) = cos(x) \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{d/dx cos(x) = -sin(x)} \tn 
% Row Count 15 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 15 (+ 0)
% Row 9
\SetRowColor{white}
product rule & y= uv \tn 
% Row Count 16 (+ 1)
% Row 10
\SetRowColor{LightBackground}
 & y'uv' + vu' \tn 
% Row Count 17 (+ 1)
% Row 11
\SetRowColor{white}
chain rule & y = y(u(x)) \tn 
% Row Count 18 (+ 1)
% Row 12
\SetRowColor{LightBackground}
 & dy/dx = dy/du . du/dx \tn 
% Row Count 19 (+ 1)
% Row 13
\SetRowColor{white}
quotient rule & y = u/v \tn 
% Row Count 20 (+ 1)
% Row 14
\SetRowColor{LightBackground}
 & y' = u'v - uv'/v\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 21 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{rewrite gradient of line: m= f(x+h) - f(x)/h \newline  \newline scalar product rule d/dx (ku(x)) = ku'(x) where k is a scalar \newline derivative of a sum: d/dx. (u(x)+v(x)) = u'(x)+v'(x)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Vectors}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{sin(𝜃) = opposite/hypotenuse} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{cos(𝜃) = adjacent/hypotenuse} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{tan(𝜃0= opposite/adjacent} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{a\textasciicircum{}2\textasciicircum{}+b\textasciicircum{}2\textasciicircum{}=c\textasciicircum{}2\textasciicircum{}} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.34379 cm} x{3.63321 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Matrices}}  \tn
% Row 0
\SetRowColor{LightBackground}
C = A+B & addition/subtraction \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
𝐵 = 𝑘𝐴 & 𝑘 is scalar, 𝐴 is 𝑚 . 𝑛 matrix \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
𝐶 = 𝐴𝐵 & if A = 𝑚 . 𝑛, B = 𝑛 . 𝑘 \tn 
% Row Count 5 (+ 2)
\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}{Trig Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
y = a sin(bx + c) + d & y = a cos(bx + c) + d \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
exponential function & y = e\textasciicircum{}x\textasciicircum{} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
domain & values x can assume \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
range & values y can assume \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{amplitude = a  \newline period = 2π/b \newline horizontal shift = - c/b \newline vertical shift = d \newline  \newline {\emph{sin(x) starts at 0, cos(x) starts at one}} \newline  \newline Expon - e = eulers's constant. \newline  \newline domain/range : \_ (\textgreater{} or \textless{}) \_}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Logarithmic Differentiation}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{ln(ab) = ln(a) + ln(b)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{ln(a/b) = ln(a) - ln(b)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{ln(a\textasciicircum{}b\textasciicircum{}) = b x ln(a)} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{ln(e) = 1} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{e\textasciicircum{}ln(x)\textasciicircum{} = x} \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Area Between Curves}}  \tn
% Row 0
\SetRowColor{LightBackground}
∫f(x)dx - ∫g(x)dx & f(x) = upper function g(x0 = lower function \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Volume of Revolution & V = π ∫ y\textasciicircum{}2\textasciicircum{} dx \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Integrating Ration Functions & f'(x) = x/x\textasciicircum{}2\textasciicircum{}-1 \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Integrals}}  \tn
% Row 0
\SetRowColor{LightBackground}
∫sin(x)dx & -cos(x) + C \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
∫cos(x)dx & sin(x) + C \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
∫e\textasciicircum{}x dx & e\textasciicircum{}x\textasciicircum{} + C \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
∫1/x dx & ln(x) + C \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
∫x\textasciicircum{}n\textasciicircum{} dx & x\textasciicircum{}n+1\textasciicircum{}/n+1 + C \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
∫ln(x) dx & xln(x) - x + C \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 6 (+ 0)
% Row 7
\SetRowColor{white}
scalar rule & ∫ ku(x) dx = k∫u(x) dx \tn 
% Row Count 8 (+ 2)
% Row 8
\SetRowColor{LightBackground}
integral of a sum & ∫(u(x) + v(x))dx = ∫u(x)dx +∫v(x)dx \tn 
% Row Count 10 (+ 2)
% Row 9
\SetRowColor{white}
derivative of intergral & d/dx∫u(x)d x= u(x) \tn 
% Row Count 12 (+ 2)
% Row 10
\SetRowColor{LightBackground}
integral of derivative & ∫u'(x)dx =u (x) + C \tn 
% Row Count 14 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 14 (+ 0)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Integrals of Common Functions}}} \tn 
% Row Count 15 (+ 1)
% Row 13
\SetRowColor{white}
∫sin(nx) dx & -1/n cos(nx) +C \tn 
% Row Count 16 (+ 1)
% Row 14
\SetRowColor{LightBackground}
∫cos(nx) dx & 1/n sin(nx) = C \tn 
% Row Count 17 (+ 1)
% Row 15
\SetRowColor{white}
∫e\textasciicircum{}nx\textasciicircum{} dx & 1/n e\textasciicircum{}nx\textasciicircum{} + C \tn 
% Row Count 18 (+ 1)
% Row 16
\SetRowColor{LightBackground}
∫ln(nx)dx & 1/n ln(nx) + C \tn 
% Row Count 19 (+ 1)
% Row 17
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 19 (+ 0)
% Row 18
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Integration by Substitution}}} \tn 
% Row Count 20 (+ 1)
% Row 19
\SetRowColor{white}
\seqsplit{∫y(u(x))u'(x)dx} & ∫y(u)du \tn 
% Row Count 22 (+ 2)
% Row 20
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Integration by Parts}}} \tn 
% Row Count 23 (+ 1)
% Row 21
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{∫uv' dx = uv- ∫u'v dx} \tn 
% Row Count 24 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{∫x\textasciicircum{}n\textasciicircum{}dx = x\textasciicircum{}n+1\textasciicircum{}/n+1 + C only applies when n does NOT equal -1}} \newline  \newline {\bf{when n= -1, ∫1/x dx applies}} \newline  \newline Indefinite Integral: no numbers at top of bottom. \newline  \newline Definite Integral: solve for a number that represents the areas under the curve from x=a to x=b \newline no integration constant in this situation}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{rules}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{product rule}}: x multiplied together in different forms eg. y = e\textasciicircum{}2\textasciicircum{}e\textasciicircum{}x\textasciicircum{} \newline  \newline {\bf{chain rule}}:  \newline inner function u(x) \newline outer function: y(u) \newline  \newline looking for function within a function eg. y=ln(sin(x)).  \newline {\emph{let u equal the inner function}} \newline  \newline {\bf{quotient:}} x in both the numerator and denominator eg. y = e\textasciicircum{}x\textasciicircum{}x\textasciicircum{}2\textasciicircum{} \newline  \newline {\bf{remember 1/a\textasciicircum{}n\textasciicircum{} = a\textasciicircum{}-n\textasciicircum{}}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.58804 cm} x{2.38896 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Functions \& Algebraic Structure}}  \tn
% Row 0
\SetRowColor{LightBackground}
y-intercept: where crosses y & solve for y when x = 0 \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
roots: where crosses x & solve for x when y = 0 \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
linear functions & y = mx + c \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
quadratic functions & y = ax\textasciicircum{}2\textasciicircum{} + bx + c \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
turning point & x = -b/2 . a \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
roots of quadratic & use quadratic formula \tn 
% Row Count 9 (+ 2)
% Row 6
\SetRowColor{LightBackground}
2π = 360° & radians = degrees . π/180 \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Function – can have only one output, y,  or each unique input, x. \newline Relation - can have more than one output, y, for each unique input, x. \newline  \newline may be be more than one root for a function. roots can also be called x-intercepts and zeros \newline  \newline linear: mx= gradient/slope C= y-intercept \newline  \newline quadratic: pos a = 'happy face', neg a = 'sad face'}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Explicit/Implicit}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 0 (+ 0)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Explicit:}} dependent variable is written explicitly in terms of the independent.  \newline {\emph{eg. y = 3x + 5}} \newline  \newline {\bf{Implicit:}} dependent variable is not isolated to one side of equation \newline {\emph{eg. 3x + 5 - y = 0}} \newline  \newline Explicit differentiation: when starting with implicit from that is rearrangeable, rearrange then do. \newline  \newline Implicit differentiation: relies on the chain rule. No rearranging required}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.4931 cm} x{3.4839 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Differential Equations}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{First Order Separable}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
f(x) dx = g(y) dy & put all x to one side and y to other \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 3 (+ 0)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Power \& Log Rules}}} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{a\textasciicircum{}b\textasciicircum{} . a\textasciicircum{}c\textasciicircum{} = a\textasciicircum{}b+c\textasciicircum{}} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{a\textasciicircum{}b\textasciicircum{}/a\textasciicircum{}c\textasciicircum{}=a\textasciicircum{}b-c\textasciicircum{}} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{ln(a\textasciicircum{}b\textasciicircum{})= bln(a)} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{ln(e) = 1} \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{e\textasciicircum{}ln(x)\textasciicircum{} = x} \tn 
% Row Count 9 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Decay}}} \tn 
% Row Count 10 (+ 1)
% Row 10
\SetRowColor{LightBackground}
dN/dt = -λN & N = amount of substance, t = time and λ is decay constant \tn 
% Row Count 13 (+ 3)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Newton's Law of Cooling}}} \tn 
% Row Count 14 (+ 1)
% Row 12
\SetRowColor{LightBackground}
dT/dt = -k(T-Ta) & T = Temp of object, Ta is ambient temp, t is time a k is heat transfer constant \tn 
% Row Count 17 (+ 3)
% Row 13
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 17 (+ 0)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{*Motion Problems}}} \tn 
% Row Count 18 (+ 1)
% Row 15
\SetRowColor{white}
v = ds/dt & s = position, v = velocity, a = acceleration, t= time \tn 
% Row Count 20 (+ 2)
% Row 16
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{a = dv/dt} \tn 
% Row Count 21 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{A differential equation is just a mathematical equation that involves derivatives.}} \newline  \newline can have more than one solution}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}