| Symboler | Exakta trigonometriska värden | Blandade formler | Derivator | Integraler | Gränsvärden | Komplexa tal | Trigonometri | Geometri |

Algebra

FormelAnmärkning
(a+b)^{2} = a^{2}+2ab+b^{2} Kvadratregeln
(a-b)^{2} = a^{2}-2ab+b^{2} Kvadratregeln
a^{2}-b^{2} = (a-b)(a+b) Konjugatregeln
a^{3}+b^{3} = (a+b)(a^2-ab+b^2)
a^{3}-b^{3} = (a-b)(a^2+ab+b^2)
(a+b)^3 = a^3+3a^2b+3ab^2+b^3
(a-b)^3 = a^3-3a^2b+3ab^2-b^3
(a+b)^{n} = a^n +\frac{n}{1!}a^{n-1}\hspace{6}b+\frac{n(n-1)}{2!}a^{n-2}\hspace{6}b^{2}+ \\ +\frac{n(n-1)(n-2)}{3!}a^{n-3} \hspace{6} b^{3}+...+b^{n} = \\ \sum_{k=0}^{n} {n\choose k}a^{n-k}b^k Binomialsatsen

Kvadratrötter

FormelAnmärkning
\sqrt{a}\cdot\sqrt{b}=\sqrt{ab} a≥0   b≥0
\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}} a≥0   b>0
\sqrt{a^{2}b}=|a|\sqrt{b} b≥0

Bråkräkning

FormelAnmärkning
\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b} b\neq 0
\frac{-a}{-b}=\frac{a}{b} b\neq 0
a\cdot \frac{b}{c}=a\frac{b}{c}=\frac{ab}{c} c\neq 0
\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd} b\neq 0, d\neq 0
\frac{a}{b}\ / \frac{c}{d}=\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot\frac{d}{c} =\frac{ad}{bc} b\neq 0, c\neq 0, d\neq 0
\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad+bc}{bd} b\neq 0, d\neq 0

Potensräkning

FormelAnmärkning
a^m \cdot a^n=a^{m+n}
(a^m)^n=a^{m\cdot n}
a^{b^c}=a^{(b^c)}
\frac{a^m}{a^n}=a^{m-n}
\left( \frac{a}{b} \right)^m=\frac{a^m}{b^m}
(ab)^m = a^m\cdot b^m
a=a^1
a^0=1 a \ne 0
1^n=1
a^{-x}=\frac{1}{a^x} a \ne 0
a^{1/2}= \sqrt{a}
a^{m/n}=(a^m)^{1/n}= \sqrt[n]{a^m} m,n > 0

Andragradsekvationer

Rötterna till ekvationen: x^2+px+q=0   ges av: x_{1,2} = -\frac{p}{2}\pm\sqrt{\left(\frac{p}{2}\right)^2-q}

Powered by Mattecentrum
 |  Denna sida använder cookies |  Kontakta oss |  Feedback |