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\documentclass[11pt]{article}
\usepackage{a4}
\author{Kristof Overdulve}
\title{Formularium Calculus}

\begin{document}
\maketitle


Ontbinden in factoren :
\[
x^{3} + y^{3} = (x + y)(x^{2} - xy + y^{2}) 
\]

Volume bol : 
\[ 
\frac{4}{3} \pi r^{3} 
\]

Volume kegel : 
\[ 
\frac{1}{3} \pi r^{2} h 
\]

Oppervlakte kegel : 
\[ 
\pi r \sqrt{r^{2} + h^{2}} 
\]

Vergelijking lijnstukken : 
\[ 
y - y_{1} = m (x - x_{1})
\]

\[ 
y = m x + b 
\]

Vergelijking cirkels : 
\[ 
(x - h)^{2} + (y - k)^{2} = r^{2}
\]

Afgeleiden : 
\[ 
\frac{d}{dx} (\tan x) = \frac{1}{\cos^{2} x}
\]

\[ 
\frac{d}{dx}(Bgtg x) = \frac{1}{1 + x^{2}}
\]

\[ 
\frac{d}{dx} (Bgsin x) = \frac{1}{\sqrt{1 - x^{2}}}
\]

Stelling van Lagrange :
\[ 
f'(c) = \frac{f(b) - f(a)}{b - a}
\]

Schuine asymptoten :
\[ 
m = \lim_{x \to \infty} \frac{f(x)}{x} 
\]

\[ 
b = \lim_{x \to \infty} f(x) - mx 
\]

Vergelijking van het raakvlak : 
\[ 
z = f(a,b) + \frac{\partial f}{\partial x}(x - a) + \frac{\partial f}{\partial y}(y - b)
\]

Richtingsafgeleide : 
\[
D_{u} f(x) = \vec u . \nabla f(x) 
\]

Hessiaanse matrix : 
\[
\Delta (\vec a) = \left(
\begin{array}{cc}
\frac{\partial^{2} f}{\partial x^{2}} (\vec a) & \frac{\partial^{2} f}{\partial y \partial x} (\vec a) \\
\frac{\partial^{2} f}{\partial x \partial y} (\vec a)  & \frac{\partial^{2} f}{\partial y^{2}} (\vec a) \\
\end{array}
\right)
\]


\end{document}