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http://functions.wolfram.com/14.01.09.0002.01
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UnitStep[x] == Limit[Exp[-Exp[-(x/\[CurlyEpsilon])]],
\[CurlyEpsilon] -> Plus[0]] /; x != 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Exp", "[", RowBox[List["-", RowBox[List["Exp", "[", RowBox[List["-", FractionBox["x", "\[CurlyEpsilon]"]]], "]"]]]], "]"]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]]]], "/;", RowBox[List["x", "\[NotEqual]", "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> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> ε </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mrow> <mo> + </mo> <mn> 0 </mn> </mrow> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mi> x </mi> <mi> ε </mi> </mfrac> </mrow> </msup> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ≠ </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> <apply> <limit /> <bvar> <ci> ε </ci> </bvar> <condition> <apply> <tendsto /> <ci> ε </ci> <apply> <plus /> <cn type='integer'> 0 </cn> </apply> </apply> </condition> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> x </ci> <apply> <power /> <ci> ε </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <neq /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["UnitStep", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["x", "\[CurlyEpsilon]"]]]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "/;", RowBox[List["x", "\[NotEqual]", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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