what is limit

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). The limit of a function describes how the function behaves near a point, instead of at that point. The strictest definition of a limit is that if there exists a real number L that for any positive value epsilon, no matter how small, there exists a natural number X, such that { |Aₓ - L| < epsilon, as long as x > X }, then we say A is limited by L, or L is the limit of A, written as lim (x→∞) A = L. The limit of a sequence and the limit of a function are closely related). The limit of a sequence {an} as n approaches infinity is simply the limit at infinity of a function a(n) defined on the natural numbers {n} ). The limit of a function f(x) as x approaches x0 is equal to L if the limit as n approaches infinity of f(xn) is L for every arbitrary sequence of points {xn} in X − x0 which converges to x0).