Traditional methods for solving multiuser control problems in CDMA systems do not scale well as the number of users in the system increases. Indeed, the size and complexity of the control problem generally grows exponentially with the number of users. In order to find a tractable solution to these problems we develop a wideband limit approximation for dynamic programming problems in CDMA systems. This approximation greatly simplifies the state space and evolution equations for the users in a CDMA cell. The simplified evolution dynamics can then be used to construct a dynamic program that solves for the optimal wideband power control. This wideband convergence result holds for a number of different linear multiuser receiver structures including the MMSE and matched filter receivers.