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\vspace*{.3in}
\noindent{\bf Beals, page 25 \#6:}
Let $f_n:\R\to\R$ be the `tent' function.
$$
f_n(x) = \left\{\begin{array}{rcl}
n^2x & \mbox{if} & 0\leq x \leq 1/n \\
2n - n^2 x & \mbox{if} & 1/n\leq x\leq 2/n \\
0 & \mbox{otherwise} &
\end{array}\right.
$$
Then
$$
\liminf \int f_n(x) = \liminf 1 > 0 = \int 0 = \int \lim f_n = \int \liminf
f_n.
$$
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