In the last years, recursive functions over the reals [Moore] have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes [Campagnolo]. However, one of the operators introduced in the seminal paper by Cris Moore (in 1996), the minimalization operator, has not be considered: (a) although differential recursion (the analog counterpart of classical recurrence) is, in some extent, directly implementable in the General Purpose Analog Computer of Claude Shannon, analog minimalization is far from physical realizability, and (b) analog minimalization was borrowed from classical recursion theory and does not fit well the analytic realm of analog computation. In this paper we show that a most natural operator captured from Analysis - the operator of taking a limit - can be used properly to enhance the theory of recursion over the reals, providing good solutions to puzzling problems raised by the original model. Moreover, we show that the classical halting problem is analog solvable, a result that has some impact on the computational power of continuous dynamic systems. The talk reports ongoing joint work with J. Félix Costa.