$\newcommand{\ds}{\displaystyle}$ $\newcommand{\Rr}{\mathbb{R}}$
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\( \frac{\sqrt{2x}}{3} \)
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\( \sqrt[n]{x_1^2+3} \)
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\(
\mathbb{R}, \mathbb{R} \setminus \mathbb{Q}
\)
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\( \limsup x_n \), \( \liminf x_n \)
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\( \int_0^1 f(x)dx = \lim_{t \to 0^+} \int_t^1 f(x)dx \)
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\[ \int_0^1 f(x)dx = \lim_{t \to 0^+} \int_t^1 f(x)dx\]
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\(\infty \)
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\(x_1, x_ 2, \ldots, x_n\), \(x_1 + x_2 + \cdots + x_n\)
and
\(\sum_{k=1}^n x_k\)
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\(\overline{\int_a^b} f \)
and
\(\underline{\int_a^b f}\)
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\(
|x| = \begin{cases}
x & \text{if}\ x > 0 \\
0 & \text{if}\ x=0 \\
-x& \text{if}\ x < 0
\end{cases}
\)