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                <term xml:lang="en">Teachers’ and Students’ practices at university level</term>
                <term xml:lang="en">Teaching and learning of analysis and calculus</term>
                <term xml:lang="en">Limit of a function</term>
                <term xml:lang="en">Discursive proximities</term>
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              <p>The introduction of the formal definition of the limit of a function during the first year of university is a source of many difficulties for students. In this exploratory research, we study the discourse of lecturers when they introduce this notion. To do so, we determine the ‘relief’ of the notion of limit, resulting from the combination of epistemological, curricular and cognitive studies. This relief enables us to envisage ‘proximity opportunities’, that is possible attempts to bring together students' prior knowledge and the notion of the limit. We demonstrate the value of using these tools by studying the discourse of one particular teacher, which enables us to identify the discursive proximities that he actually attempted.</p>
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