  In this paper we examine the zero and first order eigenvalue fluctuations for
the $\beta$-Hermite and $\beta$-Laguerre ensembles, using the matrix models we
described in \cite{dumitriu02}, in the limit as $\beta \to \infty$. We find
that the fluctuations are described by Gaussians of variance $O(1/\beta)$,
centered at the roots of a corresponding Hermite (Laguerre) polynomial. We also
show that the approximation is very good, even for small values of $\beta$, by
plotting exact level densities versus sum of Gaussians approximations.
