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Limits to Infinity

  • Ethan D. Bloch
Chapter

Abstract

When we studied limits of functions in Chapter 3, we often considered expressions of the form “ \(\lim\limits_{x\rightarrow c}f(x) = L\),” where the symbols c and L both denoted real numbers. However, it is also possible to consider limits involving not only real numbers, but limits to “infinity” and “negative infinity,” which are written \(\lim\limits_{x\rightarrow \infty}f(x) = L\) and \(\lim\limits_{x\rightarrow -\infty}f(x) = L\), and \(\lim\limits_{x\rightarrow c}f(x) = \infty\), and \(\lim\limits_{x\rightarrow c}f(x) = -\infty\). It is also possible to combine these two types of limits, for example \(\lim\limits_{x\rightarrow \infty}f(x) = \infty\). In all of the types of limits that involve ∞ and –∞, it is important to recognize that the symbols “∞” and “–∞” are not real numbers, but are rather a shorthand way of indicating that something is growing without bound either in the positive direction or in the negative direction.

Keywords

Real Number Unbounded Interval Computing Limit Historical Remark Vertical Asymptote 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Businees Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentBard CollegeAnnandale-on-HudsonUSA

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