Difference between revisions of "E^x is greater than 1+x for nonzero real x"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1|next=e^x is less than 1/(1-x) for nonzero real x less than 1}}: 4.2.30 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1|next=e^x is less than 1/(1-x) for nonzero real x less than 1}}: $4.2.30$ |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:31, 23 December 2016
Theorem
The following formula holds for nonzero $x \in \mathbb{R}$: $$e^x > 1+x,$$ where $e^x$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.2.30$
