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A compact system of inequalities for the standard limits in the theory of limits
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UDC: 514.116
Publication Language: English
Stuc. intelekt. 2013; 18(2):63–70
Abstract: The purpose of the paper is an alternative way of obtaining of the standard limits in the elementary theory of limits. The approach uses two double inequalities xe^-x ≤ sin x ≤ xe^x and xe^-x ≤ shx ≤ xe^x and the limit transition. The method is applied to both standard limits simultaneously, that makes the theory more universal. Apart from that our theory gives many new representations of the standard limits (total number is 37).
Keywords: theory of limits, standard limits, function, sine, hyperbolic sine, method, inequalities, standard limits, limit transition
References:
- Kudriavtsew L.D. Маtematichesky analiz. Том I., Nаukа,1970. – 571 p.
- Ilyin V.А., Pozdniak E.G. Оsсnowy mаtematicheskogo analiza, tом 1, Izd. FML, Моskwa, 1956. – 472 p.
- Mironenko L.P. Ekvivalentnost standartnih predelov v teoryi predelov// Iskustvenyi intellekt, 2, 2012 –P. 123-128.
- Mironenko L.P., Petrenko I.V. Standartnie predeli i metod neopredelennih koefficientov// skustvenyiintellekt, 3, 2012 – P. 284-291.
- Fihtengolts G.М. Кurs differentsialnogo i integralnogo ischislenia, tом 1, Nauka, «FML», 1972. – 795 p.
- Gursa E. Кurs mаtematicheskogo analiza, tом 1, Gosudarstvennoe techniko-tworcheskoe iezdatelstvo –Моskwa, 1933. – 368 p