Many investigations have been carried out with the objective of identifying the difficulties that students have in the learning process of the different mathematical concepts. Some studies have highlighted that the process of teaching mathematical knowledge by teachers in secondary and secondary education in Colombia, has been limited to a minimalist expression of algebraic processes that in no way contribute to the understanding and appropriation of these concepts of origin abstract. Students who enter the various engineering programs in the university must immediately face a Differential Calculus course, which will demand from the student a whole series of competences around the numerical, variational and spatial thoughts. It is in this scenario where we seek to identify the epistemological obstacles presented by the students of the Faculty of Engineering programs at the beginning of the academic training process at the UFPS. An instrument was designed that incorporates a series of activities that use diverse registers of semiotic representation tending to determine the level of appropriation that the students have around the concepts of limit and continuity. From the findings it is highlighted that students assume the concepts of limit and continuity as equals.