Formally defined, a function has a finite limit at point if, for all, there exists such that whenever. Ī real-valued function is said to have a limit if, as its argument is taken arbitrarily close to, its value can be made arbitrarily close to. For a sequence indexed on the natural number set, the limit is said to exist if, as, the value of the elements of get arbitrarily close to. Limits can be defined for discrete sequences, functions of one or more real-valued arguments or complex-valued functions. What are limits? Limits, a foundational tool in calculus, are used to determine whether a function or sequence approaches a fixed value as its argument or index approaches a given point.
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