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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Inequalities





http://functions.wolfram.com/01.03.29.0005.01









  


  








Input Form





Abs[x]/4 < Abs[E^x - 1] < (7 Abs[x])/4 /; 0 < Abs[x] < 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["Abs", "[", "x", "]"]], "4"], "<", RowBox[List["Abs", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", "x"], "-", "1"]], "]"]], "<", FractionBox[RowBox[List["7", " ", RowBox[List["Abs", "[", "x", "]"]]]], "4"]]], "/;", RowBox[List["0", "<", RowBox[List["Abs", "[", "x", "]"]], "<", "1"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mn> 4 </mn> </mfrac> <mo> &lt; </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <msup> <mi> &#8519; </mi> <mi> x </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> x </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <apply> <abs /> <ci> x </ci> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <abs /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <abs /> <ci> x </ci> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <abs /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["Abs", "[", "x", "]"]], "4"], "<", RowBox[List["Abs", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", "x"], "-", "1"]], "]"]], "<", FractionBox[RowBox[List["7", " ", RowBox[List["Abs", "[", "x", "]"]]]], "4"]]], "/;", RowBox[List["0", "<", RowBox[List["Abs", "[", "x", "]"]], "<", "1"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29