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\noindent {\bf Problem statement} If $n$ is sufficiently large, the
following functions of $n$ can be arranged in an increasing order, so
that each function is very much larger than the one preceding
it. List the functions below in order of size from smallest to
largest.

$$ n\,;\ \ n^n\,;\ \ \ln n\,;\ \ 4^n\,;\ \ 2^n\,;\ \ n\ln n\,;\ \
2^{(n^2)}\,;\ \ \sqrt{n^6+1}\,;\ \ (n^3+1)^{2/3}\,.$$

\noindent Where would $n!$ fit in this list?









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