Keyword: «surrounding of finite and infinite points»

The paper is devoted to teaching theory of limits in the course of mathematical analysis and the problems that arise in presenting educational material. To master the recording skills of the Cauchy function limit determination in the language «epsilon-delta», the authors propose a table that addressed all possible argument aspirations, written through the surroundings and intervals; provide definitions of the function limit for all cases reviewed in the table and explain in detail the content and meaning of these basic definitions on the examples of tasks. The authors offer the table that summarizes the uncertainties and shows the ways of their elimination. Calculation method of all kinds of limits on a wide range of tasks is also illustrated. The paper can be useful to lecturers and first-year students.