Analysis of student’s mental structures when incorrectly calculating the limit of function

In this paper, the authors attempt to make the analysis of unacceptable and missed student responses when calculating a limit of functions. Based on the collected data and derived conclusions, relying on APOS theory and the SOLO taxonomy, we estimate that the concept of limit values and processes with that concept (but not procedurally using this concept) for the majority of the student population is acceptable with considerable difficulty. А reconstruction is offered of student?s mental images using categorical terms RBC + C theory of abstraction and Sfard?s theoretical model for the learning of mathematical concepts.