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|<ε whenever 0<|x-a|<δ. ----------- 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 in general) and are used to define continuity, derivatives, and integrals. ----------- 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, and are used to define continuity, derivatives, and integrals.