In this paper we study several notions of approximability of functions in the framework of the BSS model. Denoting with ϕ _M ^δ the function computed by a BSS machine M when its comparisons are against −δ rather than 0, we study classes of functions f for which ϕ _M ^δ → f in some sense (pointwise, uniformly, etc.). The main equivalence results show that this notion coincides with Type 2 computability when the convergence speed is recursively bounded. Finally, we study the possibility of extending these results to computations over Archimedean fields.