# Formule

Ključne reči: matematika, formule

## Opšte informacije

$\left|a\right|$

## Teorija brojeva

$\mathrm{ℕ}\subset \mathrm{ℤ}\subset \mathrm{ℚ}\subset \mathrm{ℝ}\subset \mathrm{ℂ}$

$\mathrm{ℙ}=\left\{2,3,5,7,\dots \right\}$
$a|m⇔n·a=m$
$\left(m;n\right)=l;\left[m;n\right]=k$
$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

## Binomna teorema

${\left(a+b\right)}^{n}$

## Kombinatorika

${P}_{n}=n!$
${C}_{n}^{k}=\left(\genfrac{}{}{0}{}{n}{k}\right)$
${V}_{n}^{k}=\frac{n!}{\left(n-k\right)!}$

## Skupovi

$A\cup B=B\cup A$
$\left|A\cup B\cup C\right|$
$A×B$
$\rho \subseteq AxA$

## Logika

$a\vee b=b\vee a$

## Polinomi

${\left(a+b\right)}^{2}$

## Nizovi

${a}_{n}={a}_{a}+\left(n-1\right)d$
${a}_{n}={a}_{1}\cdot {q}^{n-1}$

## Logaritam

$lo{g}_{a}x=\frac{lo{g}_{b}x}{lo{g}_{b}a}$

## Stepenovanje

$a·a·a={a}^{3}$

## Korenovanje

$\sqrt[n]{a}=b⇒{b}^{n}=a$

## Proporcije

$a:b=c:d$

## Nejednačine

$f\left(x\right)

## Jednačine

$a{x}^{2}+bx+c=0$
$a{x}^{3}+b{x}^{2}+cx+d=0$
$\sqrt[n]{x}=a$

## Kompleksni brojevi

${z}^{n}$
${z}_{k}=\sqrt[n]{a+ib}$

## Interest Calculation

$k=T·\frac{p}{100}$

## Matrice

$C=A+B$
$C=A·B$

## Trigonometrija

$\frac{a}{sin\alpha }=\frac{b}{sin\beta }=\frac{c}{sin\gamma }$

${c}^{2}={a}^{2}+{b}^{2}-2ab\phantom{\rule{thinmathspace}{0ex}}{cos}^{2}\gamma$

$si{n}^{2}\alpha +co{s}^{2}\alpha =1$
$sin\left(\alpha ±\beta \right)$
$sin\left(2\alpha \right)$
$sin\frac{\alpha }{2}$
$sin\alpha ±sin\beta$
$sin\alpha =\frac{a}{c}$

## Dvodimenzionalni oblici

$\frac{\overline{{B}_{1}{B}_{2}}}{\overline{{B}_{2}{B}_{3}}}=\frac{\overline{{A}_{1}{A}_{2}}}{\overline{{A}_{2}{A}_{3}}}$

## Vektori

$\stackrel{\to }{a}·\stackrel{\to }{b}=|\stackrel{\to }{a}||\stackrel{\to }{b}|cos\alpha$
$\stackrel{\to }{c}=\stackrel{\to }{a}×\stackrel{\to }{b}$

## Analitička geometrija u ravni

$d=\overline{|{P}_{1}{P}_{2}|}$
${x}^{2}+{y}^{2}={r}^{2}$
$y=kx+n$
$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$

## Važne funkcije

$y=ax+b$
$y=a{x}^{2}+bx+c$
$y=a{x}^{3}+b{x}^{2}+cx+d$
$y=\frac{1}{x}$
$y=\sqrt[2k]{x},k\in \mathrm{ℕ}$
$y=\sqrt[2k+1]{x},k\in \mathrm{ℕ}$
$y={a}^{x}$
$y={\mathrm{log}}_{a}x$
$y=\mathrm{sin}x$
$y=\mathrm{cos}x$
$y=\mathrm{tg}x$
$y=\mathrm{ctg}x$
$y=|x|$

## Transformacija funkcija

$f\left(x+c\right)$

## Granična vrednost

$\underset{x\to {x}_{0}}{lim}f\left(x\right)=a$

## Diferencijalni račun

$\frac{df\left(x\right)}{dx}={f}^{\text{'}}\left(x\right)$
${\left(f·g\right)}^{\prime }={f}^{\prime }·g±f·{g}^{\prime }$
$T\left(x\right)$

## Integralni račun

$\int f\left(x\right)dx=F\left(x\right)+C$
$\int cf\left(x\right)dx=c\int f\left(x\right)dx$
${\int }_{a}^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$

## Verovatnoća

$\sum _{i=1}^{n}{A}_{i}=\Omega$
$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}$
$P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$
$P\left(A\right)=\sum _{i=1}^{n}P\left(A|{B}_{i}\right)·P\left({B}_{i}\right)$
$P\left({B}_{i}|A\right)=\frac{P\left(A|{B}_{i}\right)·P\left({B}_{i}\right)}{P\left(A\right)}$
$F\left(x\right)=P\left(\xi

## Statistika

$A=\frac{\underset{i=1}{\overset{n}{\sum {x}_{i}}}}{n}$