Indeterminate form: Difference between revisions

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{{Short description|Expression in mathematical analysis}}

In [[calculus]] and other branches of [[mathematical analysis]], limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their [[limit (mathematics)|limits]]; if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an '''indeterminate form'''. More specifically, an indeterminate form is a mathematical expression involving at most two of <math>0~</math>, <math>1</math> or <math>\infty</math>, obtained by applying the [[algebraic limit theorem]] in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being sought. A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity).<ref name=":1">{{Cite web|url=http://mathworld.wolfram.com/Indeterminate.html|title=Indeterminate|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-02}}</ref> The term was originally introduced by [[Cauchy]]'s student [[Moigno]] in the middle of the 19th century.

There are seven indeterminate forms which are typically considered in the literature:<ref name=":1" />