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Inegalitatea lui Cauchy
cu
$\displaystyle\sum_{i=1}^{n}a_ib_i\le\sqrt{\sum_{i=1}^{n}a_i^2\cdot\sum_{i=1}^{n}b_i^2}$
$a_i,b_i>0,i=\overline{1,n}$
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Inegalitatea lui Minkowski
$\displaystyle\left[\sum_{i=1}^{n}(a_i+b_i)^k\right]^\frac{1}{k}\le\left(\sum_{i=1}^{n}a_i^k\right)^\frac{1}{k}+\left(\sum_{i=1}^{n}b_i^k\right)^\frac{1}{k}$
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Volumul sferei
$vol(S)=2\pi\displaystyle\int_{0}^{r}\left(\sqrt{r^2-x^2}\right)^2dx=2\pi\int_{0}^{r}(r^2-x^2)dx=2\pi\left(r^2x\Big|_0^r-\frac{x^3}{3}\bigg|_0^r\right)=\frac{4\pi r^3}{3}$
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Sa se calculeze:
$\displaystyle\int e^{\arcsin x}dx$
$ I=xe^{\arcsin x}-\displaystyle\int e^{\arcsin x}\frac{x}{\sqrt{1-x^2}}dx= xe^{\arcsin x}+\sqrt{1-x^2}\cdot e^{\arcsin x} - I $
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Vectorul de pozitie al centrului cercului inscris:
unde
$\vec{r_I}=\displaystyle\frac{a}{2p}\vec{r_A}+\frac{b}{2p}\vec{r_B}+\frac{c}{2p}\vec{r_C}$
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Relatia intre combinari, aranjamente si permutari :
$C_{n}^{k}=\dfrac{A_{n}^{k}}{P_k}$
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$\displaystyle\left[\moama da cum de le scrii fara greseala ?:P$
---
iau nota mare la BAC
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Greseli mi-au aparut destule...insa le-am tot reeditat pana mi-au iesit; secretul este: rabdarea !
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