Difference between revisions of "X less than e^x-1 less than x/(1-x) for nonzero real x less than 1"
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(Created page with "==Theorem== The following formula holds for nonzero $x \in \mathbb{R}$ with $x<1$: $$x < e^x -1 < \dfrac{x}{1-x},$$ where $e^x$ denotes the exponential. ==Proof== ==Refe...") |
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1|next=1+x greater than exp(x/(1+x)) for nonzero real x greater than -1}}: 4.2.33 | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1|next=1+x greater than exp(x/(1+x)) for nonzero real x greater than -1}}: 4.2.33 | ||
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:34, 23 December 2016
Theorem
The following formula holds for nonzero $x \in \mathbb{R}$ with $x<1$: $$x < e^x -1 < \dfrac{x}{1-x},$$ where $e^x$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.33
