http://i39.tinypic.com/2j5hxqo.jpg

I'm not sure if they're suggesting that for any complex number w, a function f with an essential singularity at $\displaystyle z_0$ has the property that $\displaystyle f \to w$ as z $\displaystyle \to z_0$. This seems intuitively to just be not true at all, but to be fair, the book's description of essential singularities is "we leave essential singularities to the exercises."