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% LaTeX Math Playground (KaTeX) \section{Euler's Identity} The most beautiful equation in mathematics: $$e^{i\pi} + 1 = 0$$ \section{Quadratic Formula} For $ax^2 + bx + c = 0$, the solutions are: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \section{Matrix Multiplication} $$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} e \\ f \end{pmatrix} = \begin{pmatrix} ae + bf \\ ce + df \end{pmatrix}$$ \section{Calculus} $$\int_0^\infty e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}$$ $$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$$ \section{Maxwell's Equations} $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$ $$\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}$$
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