Abstract
International audience In this communication, we present the results of a didactic investigation on the teaching and learning of limited developments and local approximations at the beginning of the university. Three investigations are carried out: the first, of an epistemological nature, deals with the historical and mathematical evolution of the semantic, syntactic and semiotic dimensions; the second is macro-didactic dedicated to the results of an analysis of programs, textbooks, course handouts and the third investigation is micro-didactic from which we will present the first results of the analysis of a survey addressed to 24 university teachers to decrypt the aims and didactic characteristics.