Exponential function: Inequalities (formula 01.03.29.0002)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Inequalities

http://functions.wolfram.com/01.03.29.0002.01

Input Form

x/(x + 1) < 1 - E^(-x) < x /; x > -1

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[FractionBox["x", RowBox[List["x", "+", "1"]]], "<", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "x"]]]]], "<", "x"]], "/;", RowBox[List["x", ">", RowBox[List["-", "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> <mi> x </mi> <mrow> <mi> x </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> < </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> x </mi> </mrow> </msup> </mrow> <mo> < </mo> <mi> x </mi> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> > </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <ci> x </ci> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> <ci> x </ci> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29