Difference between revisions of "E^x is less than 1/(1-x) for nonzero real x less than 1"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^x is greater than 1+x for nonzero real x|next=}}: 4.2.31 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^x is greater than 1+x for nonzero real x|next=x/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1}}: 4.2.31 |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:32, 23 December 2016
Theorem
The following formula holds for nonzero $x \in \mathbb{R}$ with $x<1$: $$e^x < \dfrac{1}{1-x},$$ where $e^x$ denotes the exponential function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.31
