E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1
From specialfunctionswiki
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 ... (previous) ... (next): 4.2.29