This publication is a methodological supplement to the textbook by L. D. Kudryavtsev "A Short Course in Mathematical Analysis" (M.: Fizmatlit, 2002), which is based on an unconventional definition of the limit of function. The brochure discusses in detail the advantages of such a definition over those commonly used in educational literature. The second part of the pamphlet analyzes the relationship between the Taylor and Newton-Leibniz formulas.