Physical Sciences and Mathematics Commons^™

Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.