Min[Subscript[x, 1], Subscript[x, 2]] == -Limit[\[CurlyEpsilon] Log[E^(-(Subscript[x, 1]/\[CurlyEpsilon])) + E^(-(Subscript[x, 2]/\[CurlyEpsilon]))], \[CurlyEpsilon] -> 0]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> min </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mtext> </mtext> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> &#949; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mi> &#949; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mi> &#949; </mi> </mfrac> </mrow> </msup> <mo> + </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mi> &#949; </mi> </mfrac> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <min /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <limit /> <bvar> <ci> &#949; </ci> </bvar> <condition> <apply> <tendsto /> <ci> &#949; </ci> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <times /> <ci> &#949; </ci> <apply> <ln /> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> &#949; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> &#949; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Min", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["Limit", "[", RowBox[List[RowBox[List["\[CurlyEpsilon]", " ", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SubscriptBox["xx", "1"], "\[CurlyEpsilon]"]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SubscriptBox["xx", "2"], "\[CurlyEpsilon]"]]]]]], "]"]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", "0"]]]], "]"]]]]]]]]

2001-10-29