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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.n one hand, the limit as n goes to infinity of a sequence a(n) is simply the limit at infinity of a function defined on the natural numbers n.
Whenever a point x is within Î´ units of c, f (x) is within Îµ units of L. In preliminary calculus, the concept of a limit is probably the most difficult one to grasp (after all, it took mathematicians 150 years to arrive at it); it is also the most important and most useful. The intuitive definition of a limit is inadequate to prove anything rigorously about it.