@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-W6PNFRTC-L
  skos:prefLabel "calculus"@en, "calcul"@fr ;
  a skos:Concept ;
  skos:narrower psr:-Q5TG69V0-9 .

psr:-XCN5KKXL-W
  skos:prefLabel "règle de L'Hôpital"@fr, "L'Hôpital's rule"@en ;
  a skos:Concept ;
  skos:broader psr:-Q5TG69V0-9 .

psr:-Q5TG69V0-9
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Indeterminate_form>, <https://fr.wikipedia.org/wiki/Forme_ind%C3%A9termin%C3%A9e> ;
  skos:definition """En mathématiques, une forme indéterminée est une opération apparaissant lors d'un calcul d'une limite d'une suite ou d'une fonction sur laquelle on ne peut conclure en toute généralité et qui nécessite une étude au cas par cas. Par exemple, on ne peut conclure de manière générale sur la limite de la somme de deux suites dont l'une tend vers + ∞ et l'autre vers − ∞. Selon les cas, cette limite peut être nulle, égale à un réel non nul, être égale à + ∞ ou − ∞ ou bien même ne pas exister. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Forme_ind%C3%A9termin%C3%A9e">https://fr.wikipedia.org/wiki/Forme_ind%C3%A9termin%C3%A9e</a>)"""@fr, """In calculus and other branches of mathematical analysis, when the limit of the sum, difference, product, quotient or power of two functions is taken, it may often be possible to simply add, subtract, multiply, divide or exponentiate the corresponding limits of these two functions respectively. However, there are occasions where it is unclear what the sum, difference, product, quotient, or power of these two limits ought to be. For example, it is unclear what the following expressions ought to evaluate to:
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\rac {0}{0}},~{\\rac {\\\\infty }{\\\\infty }},~0\\	imes \\\\infty ,~\\\\infty -\\\\infty ,~0^{0},~1^{\\\\infty },{\\	ext{ and }}\\\\infty ^{0}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>0</mn>
<br/>            <mn>0</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mn>0</mn>
<br/>        <mo>×<!-- × --></mo>
<br/>        <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <msup>
<br/>          <mn>0</mn>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>,</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <msup>
<br/>          <mn>1</mn>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>,</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtext>&nbsp;and&nbsp;</mtext>
<br/>        </mrow>
<br/>        <msup>
<br/>          <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>0</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {0}{0}},~{\\rac {\\\\infty }{\\\\infty }},~0\\	imes \\\\infty ,~\\\\infty -\\\\infty ,~0^{0},~1^{\\\\infty },{\\	ext{ and }}\\\\infty ^{0}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c2483920156c634ab600677eb289a5799279361" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:42.268ex; height:5.176ex;" alt="{\\\\displaystyle {\\rac {0}{0}},~{\\rac {\\\\infty }{\\\\infty }},~0\\	imes \\\\infty ,~\\\\infty -\\\\infty ,~0^{0},~1^{\\\\infty },{\\	ext{ and }}\\\\infty ^{0}.}"></span></dd></dl>
<br/>These seven expressions are known as <b>indeterminate forms</b>. More specifically, such expressions are obtained by naively applying the algebraic limit theorem to evaluate the limit of the corresponding arithmetic operation of two functions, yet there are examples of pairs of functions that after being operated on converge to 0, converge to another finite value, diverge to infinity or just diverge. This inability to decide what the limit ought to be explains why these forms are regarded as <b>indeterminate</b>. 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. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Indeterminate_form">https://en.wikipedia.org/wiki/Indeterminate_form</a>)"""@en ;
  skos:broader psr:-W6PNFRTC-L ;
  skos:related psr:-N06DS5VX-D ;
  dc:modified "2023-07-13"^^xsd:date ;
  a skos:Concept ;
  skos:narrower psr:-XCN5KKXL-W ;
  skos:prefLabel "indeterminate form"@en, "forme indéterminée"@fr .

psr: a skos:ConceptScheme .
psr:-N06DS5VX-D
  skos:prefLabel "limit of a function"@en, "limite"@fr ;
  a skos:Concept ;
  skos:related psr:-Q5TG69V0-9 .