The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students' abstraction processes were examined over "recognition", "building-with", "construction", and "consolidation". In the process, three problems that enable students to use their pre-knowledge were designed by the researchers to reveal the students' mathematical thinking levels, abstraction processes, and finally to improve a new structure. These problems were used in the application, and students' dialogues were video-recorded. The "semi-constructed interview" and "observation" data-collection methods were used in this process, and one of the researchers participated in the study as a "participant observer". The data was analyzed and interpreted by transcribing the video recordings into written text and grouping them into the cognitive actions of the RBC+C model. In conclusion, these students were indicated to have managed "recognizing" and "building-with" their pre-knowledge on sequence, function, and infinity, and thus constructing knowledge on limits.