Tekanan \((P)\) berbanding terbalik dengan volume \((V)\), yang dapat ditulis sebagai \(P = \frac{1}{V}\).
Persamaan kuadrat memiliki bentuk umum: \[ax^2 + bx + c = 0\]
Atau menggunakan environment equation: \[\begin{equation} E = mc^2 \end{equation}\]
Atau menggunakan
\[ ... \]:\[ \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} \]
\(x^2\)
\(a_i\)
\(\frac{a}{b}\)
\(\sqrt{x}\)
\(\sqrt[n]{x}\)
\(\sum_{i=1}^{n} i^2\)
\(\prod_{i=1}^{n} x_i\)
\(\int_{a}^{b} f(x) dx\)
\(\lim_{x \to \infty} \frac{1}{x}\)
latex \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)
latex \(f(x) = \begin{cases} 1 & \text{if } x \ge 0 \\ -1 & \text{if } x < 0 \end{cases}\)
\(\alpha, \beta, \gamma, \pi, \theta, \omega\)
\(>, <, \ge, \le, \neq, \approx, \equiv\)
\(+, -, \times, \div, \cdot, \ast, \circ\)
\(\land, \lor, \neg, \implies, \iff, \forall, \exists\)
\[x^2\]
\[a_i\]
\[\frac{a}{b}\]
\[\sqrt{x}\]
\[\sqrt[n]{x}\]
\[\sum_{i=1}^{n} i^2\]
\[\prod_{i=1}^{n} x_i\]
\[\int_{a}^{b} f(x) dx\]
\[\lim_{x \to \infty} \frac{1}{x}\]
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
\[f(x) = \begin{cases} 1 & \text{if } x \ge 0 \\ -1 & \text{if } x < 0 \end{cases}\]
\[\alpha, \beta, \gamma, \pi, \theta, \omega\]
\[>, <, \ge, \le, \neq, \approx, \equiv\]
\[+, -, \times, \div, \cdot, \ast, \circ\]
\[\land, \lor, \neg, \implies, \iff, \forall, \exists\]
Pangkat (Superscript) \[x^2\]
Subskrip (Subscript) \[a_i\]
Pecahan (Fractions) \[\frac{a}{b}\]
Akar Kuadrat (Square Root) \[\sqrt{x}\]
Akar ke-n (nth Root) \[\sqrt[n]{x}\]
Sigma (Summation) \[\sum_{i=1}^{n} i^2\]
Pi (Product) \[\prod_{i=1}^{n} x_i\]
Integral \[\int_{a}^{b} f(x) dx\]
Limit \[\lim_{x \to \infty} \frac{1}{x}\]
Matriks latex \[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
Kasus (Piecewise) latex \[f(x) = \begin{cases} 1 & \text{if } x \ge 0 \\ -1 & \text{if } x < 0 \end{cases}\]
Simbol Yunani \[\alpha, \beta, \gamma, \pi, \theta, \omega\]
Relasi \[>, <, \ge, \le, \neq, \approx, \equiv\]
Operasi Biner \[+, -, \times, \div, \cdot, \ast, \circ\]
Logika Matematika \[\land, \lor, \neg, \implies, \iff, \forall, \exists\]
##matriks \[\begin{pmatrix} x^2_{11} & x^2_{12} & x \\ c & d & 6 \\ 1 & 2 & 3 \end{pmatrix}\]
Dalam bagian ini, kita akan membahas beberapa konsep matematika penting.
Bentuk umum persamaan kuadrat adalah: \[ax^2 + bx + c = 0\] dengan \(a \neq 0\). Akar-akar persamaan ini dapat ditemukan menggunakan rumus kuadrat: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
Integral tentu dari fungsi \(f(x)\) dari \(a\) sampai \(b\) didefinisikan sebagai: \[ \int_{a}^{b} f(x) dx = F(b) - F(a) \] di mana \(F'(x) = f(x)\).
Limit fungsi \(f(x)\) ketika \(x\) mendekati \(c\) ditulis sebagai: \[ \lim_{x \to c} f(x) = L \]
Contoh matriks 2x2 adalah: \[ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \]
Fungsi nilai absolut dapat didefinisikan sebagai fungsi piecewise: \[ |x| = \begin{cases} x & \text{jika } x \ge 0 \\ -x & \text{jika } x < 0 \end{cases} \]
Dalam fisika, kita sering menggunakan simbol Yunani seperti \(\alpha\), \(\beta\), dan \(\gamma\). Konstanta pi (\(\pi\)) juga sangat penting.
##greek latter upercase \[\Gamma, \Delta, \Sigma\]
Contoh 1: \[\begin{align} y &= mx + c \\ y_1 &= mx_1 + c \\ y_2 &= mx_2 + c \end{align}\]
Contoh 2: \[\begin{align*} a^2 + b^2 &= c^2 \\ (3)^2 + (4)^2 &= 5^2 \\ 9 + 16 &= 25 \end{align*}\]
Contoh 3: \[\begin{eqnarray} (a+b)^2 &=& a^2 + 2ab + b^2 \\ (a-b)^2 &=& a^2 - 2ab + b^2 \end{eqnarray}\]
Contoh 4: \[\begin{eqnarray} \bar{x} &=& \sum_{i=1}^n \frac{x_i}{n} \\ &=& \frac{1}{n} \sum_{i=1}^n x_i \\ &=& \frac{1}{n} \sum_{i=1}^n x_i \end{eqnarray}\]
\[f(x; \alpha, \beta) = \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha - 1} e^{- \frac{x}{\beta}}\] \[ f(x; \mu, \sigma) = \frac{1}{\sqrt{2\pi\sigma^2}}\]