Zero-bounded limits as a special case of the squeeze theorem for evaluating single-variable and multivariable limits

• Autores: Eleftherios Gkioulekas
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 4, 2013, págs. 595-609
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.742148
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• Resumen

  • Many limits, typically taught as examples of applying the �squeeze� theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful for both single-variable limits and multidimensional limits. A comprehensive treatment of multidimensional limits and continuity is also outlined.