  Let $U$ be a bounded open subset of the complex plane and let $A_{\alpha}(U)$
denote the set of functions analytic on $U$ that also belong to the little
Lipschitz class with Lipschitz exponent $\alpha$. It is shown that if
$A_{\alpha}(U)$ admits a bounded point derivation at $x \in \partial U$, then
there is an approximate Taylor Theorem for $A_{\alpha}(U)$ at $x$. This extends
and generalizes known results concerning bounded point derivations.
