Abstract. In the paper, methodical approaches to the study of continuity of functions are presented, knowledge of which has a significant impact on both the mathematical and methodological training of future specialists. The primary problem for understanding the concept of continuity is the formation of visually-intuitive understanding. The level of assimilation of concepts should be evaluated, basically, at the level of identification, but not by the ability to reproduce definitions of continuity of a function at a point.
Keywords: Mathematics, algebra, statistics, theory and practice, graphics, speed, time, differentiation.
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