Limits to Infinity

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
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