Given a function f(x), we can look how f(x) grows when x → ∞. If there is a limit for x → ∞, we have a horizontal asymptote. For example limx→∞ arctan(x) = π/2. We can also reach infinity vertically. If …

There are four symbols discussed here— an indeterminate numerical quantity È, infinity ¥, complex infinity ¥, and directed infinity in the complex plane z ¥. They are defined as follows: Indeterminate È …

Is there only one “size” of infinity? In order to prove that other sized of infinity exist we must show that there is a set of numbers that is not countable.

Beginning with Aristotle, and until the nineteenth century, the vast majority of major philosophers and mathematicians rejected the notion of the actual infinite. They argued that the only sensible notion is …

A limit at infinity occurs when the independent variable increases or decreases without bound. So, limits at infinity tell us how a function is behaving as its x-values get increasingly more positive or negative.

2 Limits at In nity De nition 2.2.3. We say the limit as x appr. s in nity is L, written lim f(x) = x!1 L, if for some x large enough the graph of y = f(x) moves closer and closer to th. line y = L as one moves to …

limits at infinity. We call the behavior of a function as its input approaches infinity the asymptotic behav gument x → ±∞. The function can either approach ±∞, meaning that it increases or decreases …