## About: Indeterminate formGotoSponge NotDistinct Permalink

An Entity of Type : yago:Matter100020827, within Data Space : dbpedia.org associated with source document(s)

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 it is said to assume an indeterminate form. More specifically, an indeterminate form is a mathematical expression involving 0, 1 and , 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 and thus does not yet determine the limit being sought. The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century.

AttributesValues
rdf:type
rdfs:label
• Indeterminate form
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 it is said to assume an indeterminate form. More specifically, an indeterminate form is a mathematical expression involving 0, 1 and , 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 and thus does not yet determine the limit being sought. The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century.
foaf:isPrimaryTopicOf
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
sameAs
dbp:wikiPageUsesTemplate
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 it is said to assume an indeterminate form. More specifically, an indeterminate form is a mathematical expression involving 0, 1 and , 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 and thus does not yet determine the limit being sought. 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 x approaches 0, the ratios , , and go to , 1, and 0 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 0, 1, 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 0 as x 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, because any limit that gives rise to this form will diverge to infinity. Expressions that arise in other ways than by applying the algebraic limit theorem may assume the same form as one of the indeterminate forms. It is not appropriate, however, to call these expressions "indeterminate forms" outside the context of determining limits.The most common case is , which may, for example, arise from substituting for in the equation . This expression is undefined, as is division by zero in general.The other case 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 .
Faceted Search & Find service v1.17_git51 as of Sep 16 2020

Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About

OpenLink Virtuoso version 08.03.3319 as of Dec 29 2020, on Linux (x86_64-centos_6-linux-glibc2.12), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software