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Infinite limits intro

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Matrix Inverse Calculator 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. Limits can be defined for discrete sequences, functions of one or more real-valued arguments or complex-valued functions. For a sequence indexed on the natural number setthe limit is said to exist if, asthe value of the elements of get arbitrarily close to. A real-valued function is said to have a limit if, as its argument is taken arbitrarily close toits value can be made arbitrarily close to. Formally defined, a function has a finite limit at point if, for allthere exists such that whenever. This definition can be further extended for or being taken to infinity and to multivariate and complex functions. In principle, these can result in different values, and a limit is said to exist if and only if the limits from both above and below are equal:.

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