Difference between revisions of "E^x is greater than 1+x for nonzero real x"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds for nonzero $x \in \mathbb{R}$: $$e^x > 1+x,$$ where $e^x$ denotes the exponential. ==Proof== ==References== * {{BookReference|Han...") |
|||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
* {{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 | ||
| + | |||
| + | [[Category:Theorem]] | ||
Revision as of 20:02, 7 June 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
