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.
Eleftherios Gkioulekas email@example.com (2013) Zero-bounded limits as a special case of the squeeze theorem for evaluating single-variable and multivariable limits, International Journal of Mathematical Education in Science and Technology, 44:4, 595-609, https://doi.org/10.1080/0020739X.2012.742148
International Journal of Mathematical Education in Science and Technology