limitsfrom

Limitsfrom is a term used to describe the process of taking a limit of a function as the variable approaches a target point from a specified direction. It is not a standard mathematical notation, but rather an informal label that appears in some teaching materials and in a few symbolic computation libraries as a mechanism to compute one-sided limits when a side parameter is provided.

In typical calculus, one uses the one-sided limit notations lim_{x→a^-} f(x) and lim_{x→a^+} f(x) to denote approaching a from the left or the right. The concept of limitsfrom, by contrast, emphasizes the direction in a unified form. In practice, a function or tool labeled as limitsfrom usually accepts a function f, a target point a, and a direction specification such as "left" or "right" (or equivalent indicators), and it returns the corresponding one-sided limit if it exists. If the relevant one-sided limit does not exist, the output typically indicates undefined or diverges.

Existence and behavior of limitsfrom follow the same mathematical rules as one-sided limits: a one-sided limit exists when the function approaches a finite value (or infinity) along the prescribed path. If both left and right limits exist and are equal, the standard (two-sided) limit exists as well.

See also: limit, one-sided limit, left-hand limit, right-hand limit, directional limit.