Limits to Infinity

  • Ethan D. Bloch


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.


Real Number Unbounded Interval Computing Limit Historical Remark Vertical Asymptote 
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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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