Difference between revisions of "E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds for $x \in (0,1)$: $$\exp \left( -\dfrac{x}{1-x} \right) < 1-x < e^{-x},$$ where $\exp$ denotes the exponential. ==Proof== ==Refe...") |
|
(No difference)
|
Revision as of 04:18, 7 June 2016
Theorem
The following formula holds for $x \in (0,1)$: $$\exp \left( -\dfrac{x}{1-x} \right) < 1-x < e^{-x},$$ where $\exp$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions: 4.2.29