This paper presents a theoretical study of the fading memory phenomenon in a TaOx-based memristor, manufactured and modeled at Hewlett-Packard Labs. Specifically, we derive a set of equations that can be used to characterize its steady-state response to a high-frequency zero-mean periodic square-wave voltage stimulus. Our results reveal a hidden property of the Dynamic Route Map (DRM) system-theoretic analysis tool, i.e. its capability to predict accurately the mean value of the state variable oscillation in first-order non-volatile memristors, at steady-state, as a function of the input amplitude alone. This DRM property may be useful in real-world memristor-based applications, where voltage pulses are most often employed to modulate the states of practical memristor devices.