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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 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 , or , 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

Attributes	Values
rdfs:label	Indeterminate form (en)
rdfs:comment	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 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 , or , 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 (en)
sameAs	Indeterminate form
dbp:wikiPageUsesTemplate	dbt:Block_indent dbt:Main dbt:Radic dbt:Redirect dbt:Reflist dbt:Sfrac dbt:Sup dbt:Var dbt:Calculus_topics
Subject	Limits (mathematics)
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Indeterminate_form?oldid=1054384831&ns=0
Wikipage page ID	366723 (xsd:integer)
page length (characters) of wiki page	16731 (xsd:nonNegativeInteger)
Wikipage revision ID	1054384831 (xsd:integer)
Link from a Wikipage to another Wikipage	François-Napoléon-Marie Moigno Projective linear group Undefined (mathematics) Analytic function Augustin-Louis Cauchy Calculus Limits (mathematics) Division by zero Zero to the power of zero Continuous function Function (mathematics) Indeterminate (variable) Indeterminate equation Indeterminate system Derivative Extended real number line Infinitesimal L'Hôpital's rule Limit (mathematics) Limit of a function Limit point Numerical analysis Natural logarithm Point at infinity Real number
has abstract	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 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 , or , 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). 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: The most common example of an indeterminate form occurs when determining the limit of the ratio of two functions, in which both of these functions tend to zero in the limit, and is referred to as "the indeterminate form ". For example, as approaches , the ratios , , and go to , , and respectively. In each case, if the limits of the numerator and denominator are substituted, the resulting expression is , which is undefined. In a loose manner of speaking, can take on the values , , or , and it is easy to construct similar examples for which the limit is any particular value. So, given that two functions and both approaching as approaches some limit point , that fact alone does not give enough information for evaluating the limit Not every undefined algebraic expression corresponds to an indeterminate form. For example, the expression is undefined as a real number but does not correspond to an indeterminate form; any defined limit that gives rise to this form will diverge to infinity. An expression that arises by ways other than applying the algebraic limit theorem may have the same form of an indeterminate form. However it is not appropriate to call an expression "indeterminate form" if the expression is made outside the context of determining limits.For example, which arises from substituting for in the equation is not an indeterminate form since this expression is not made in the determination of a limit (it is in fact undefined as division by zero).Another example is the expression . Whether this expression is left undefined, or is defined to equal , depends on the field of application and may vary between authors. For more, see the article Zero to the power of zero. Note that and other expressions involving infinity . (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Indeterminate_form
is Wikipage redirect of	List of indeterminate forms Equivalent infinitesimal Indeterminate expression Indeterminate expressions Indeterminate forms 0/0 0 divided by 0 0 × ∞ 0×∞ 0÷0 1^∞ Equivalent infinitesimals Indeterminate number ∞^0 ∞/∞ ∞0 ∞ - ∞ ∞−∞ Zero divided by zero
is Link from a Wikipage to another Wikipage of	Flight dynamics (spacecraft) Form Local ring Log probability NaN Numerical differentiation 0 Argument (complex analysis) Brāhmasphuṭasiddhānta Cauchy distribution Glossary of calculus Glossary of engineering: A–L James A. D. W. Anderson Division by zero Chebyshev polynomials Clearing denominators Degenerate distribution List of indeterminate forms List of real analysis topics Complex measure List of calculus topics Equivalence Equivalent infinitesimal Gabriel's Horn Goldman–Hodgkin–Katz flux equation Improper integral Indeterminate Indeterminate (variable) Indeterminate equation Indeterminate expression Indeterminate expressions Indeterminate forms Indeterminate system Expected value Exponentiation Extended real number line Extraneous and missing solutions

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