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\documentclass{article}
\begin{document}
\begin{equation}
\lim_{x\to0}\frac{\sqrt{1+x} - 1}{x} =
\lim_{x\to0}\frac{(\sqrt{1+x} - 1)(\sqrt{1+x} + 1)}{x(\sqrt{1+x} + 1)} =
\lim_{x\to0}\frac{1}{\sqrt{1+x} + 1} = \frac{1}{2}
\end{equation}
\begin{equation}
\frac{\partial^2 U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2} = 0\quad
\Longrightarrow\quad
U_M = \frac{1}{4\pi}\oint\limits_\Sigma\frac{1}{r}\frac{\partial U}{\partial n}
\,ds - \frac{1}{4\pi}\oint\limits_\Sigma\frac{\partial\frac{1}{r}}{\partial n}
U\,ds
\end{equation}
\end{document}
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