The difficulties in mathematics in higher education have been much discussed in several studies in mathematics education. Concerning the calculation, the research points to the fact that the teaching and learning of the concepts involved have many issues that deserve to be deepened. So we have the problem of this research question: what epistemological obstacles are present in the construction of the concept of limit of a real function real values? From the above, we propose to identify the epistemological obstacles (BACHELARD, 1996; BROUSSEAU, 1986) in the construction of the concept of limit real function of a real variable from obstacles listed by Cornu (1983), Sierpinska (1985) and Rezende (1994). To achieve this goal, we use the observation of lessons of discipline Calculus I and questionnaires to collect data that allowed us to analyze the barriers identified by these authors are also present and how they appear in the current student body of our region. The research is focused on the context of the training of mathematics teachers of public HEIs in Bethlehem, more specifically, with students who were attending the course Calculus I, Universidade Federal do Pará (UFPA), Universidade do Estado do Pará (UEPA) and the Instituto Federal do Pará (IFPA). The theoretical framework used in this research consists of a historical survey of the concept of limit is fundamental to the identification of obstacles concerning the development of this concept, an overview of research on the teaching and learning of limit, portraying the main difficulties and the different ways to minimize them, and a discussion about the epistemological obstacles identified by other authors. Evidence, with it, the epistemological obstacles are still present among the students. In an attempt to overcome them offer some pointers for teaching limit real function to a real variable, presented in thematic lines, intertwining the assumptions of history and didactics of mathematics.
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