This paper reports findings of an explorative study that examine the effectiveness of a GeoGebra-based dynamic applet in supporting students' construction of the formal definition of the limit of a sequence or convergence. More specifically, it is about how the use of the applet enables students to make connections between the graphical representation and the formal definition. There are several core components that one can extract from the definition and the applet is specifically designed to help students with the components. Relevant student data from the study are presented with respect to these components. The significance of the applet and further research directions are discussed at the end with reference to existing research.