Limits

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus and mathematical analysis, used to define continuity, derivatives, and integrals. Formally, a limit is defined as follows: let ƒ be a function defined on some open interval containing a, except possibly at a itself, and let L be a real number. We say that ƒ has a limit L at a, and write lim_(x→a)ƒ(x)=L provided that for every ε>0 there exists a δ>0 such that |ƒ(x)-L|