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Reaaliluvut: $\mathbb{R}$

Tekstin kirjoittaminen kaavariville:
\[
\left(x - \frac{a+1}{a}\right)^2 \ge 0\quad \text{ja $= 0$ vain, jos $ax = a+1$}.
\]

Kaavaketjun jakaminen useille riveille:
\[
\begin{split}
\cos 2x &= \cos^2 x - \sin^2 x \\
&= 1 - 2\sin^2 x \\
&= 2\cos^2 - 1
\end{split}
\]

Pitkän kaavan jakaminen usealle riville:
\begin{multline*}
(a+b)^{10} = a^{10} + 10a^9b + 45a^8b^2 \\
+ 120a^7b^3 + 210a^6b^4 + 252a^5b^5 + 210a^4b^6 \\
+ 120a^3b^7 + 45a^2b^8 + 10ab^9 + b^{10}
\end{multline*}

Kaavaryhmä:
\begin{align*}
\int \sin x\,dx &= -\cos x + C \\
\int \arcsin x\,dx &= x\arcsin x + \sqrt{1-x^2} \\
\int \cos x\,dx &= \sin x + C \\
\int \frac{1}{\sqrt{1-x^2}}\,dx &= \arcsin x + C \\
\end{align*}

Yhtälöryhmä:
\[
\left\{
\begin{aligned}
x + 2y + 3z &= 10 \\
4x + 5y + 6z &= 11 \\
7x + 8y + 9z &= 12
\end{aligned}
\right.
\]

Matriisi ja determinantti:
\[
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\qquad
\begin{vmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{vmatrix}
\]

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