In calculus, a limit is a fundamental concept that describes how a function behaves near a point, instead of at that point. More specifically, a limit tells us the value that a function approaches as its inputs get closer and closer to some number.
- A limit is a method of determining what the function "ought to be" at a particular point based on what the function is doing as we get close to that point.
- It is used to define integrals, derivatives, and continuity in calculus and mathematical analysis.
- Limits are concerned with the behavior of the function at a particular point.
The formal definition of a limit is as follows:
- Let $$f$$ be a real-valued function and $$c$$ be a real number. The limit is defined as $$\lim_{x \to c} f(x) = L$$, where the function $$f(x)$$ approaches the limit $$L$$ as $$x$$ approaches $$c$$.
Limits can be evaluated analytically and graphically. Analytically, we can use direct substitution or algebraic manipulation to find the limit of a function. Graphically, we can observe the behavior of the function as $$x$$ approaches a certain value.
