Методические аспекты подходов к преподаванию теории пределов функций

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Методические аспекты подходов к преподаванию теории пределов функций
Гуманитарный вестник # 5·2016 11
Methodical aspects of approaches to teaching theory
of function limits
© . Akhmetova, A.V. Kosova, I.N. Pelevina
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article discusses some aspects of teaching the theory of limits in the course of math-
ematical analysis and the problems arising in presenting the educational material. To
solve the difficulties in recording the neighborhood of finite and infinite points at differ-
ent argument tendencies a table is offered that addresses all possible argument tenden-
cies, described through the neighborhoods and intervals, and the Cauchy definitions of
the function limit for all cases presented in the table are given. The table summarizing
the uncertainties and ways to address them in finding limits of functions is also given.
The techniques of calculating all possible limits are illustrated on a wide range of tasks.
Keywords: Cauchy and Heine function limit, neighborhood of finite and infinite points,
evaluation of indeterminate forms.
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