Exponential function: Inequalities (formula 01.03.29.0001)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Inequalities

http://functions.wolfram.com/01.03.29.0001.01

Input Form

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

Standard Form

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