Difference between revisions of "X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1"
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Latest revision as of 00:33, 23 December 2016
Theorem
The following formula holds for nonzero $x \in \mathbb{R}$ with $x<-1$: $$\dfrac{x}{1+x} < 1-e^{-x} < x,$$ where $e^{-x}$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.32