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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(Created page with "==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==...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^x is less than 1/(1-x) for nonzero real x less than 1|next=}}: 4.2.32 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=E^x is less than 1/(1-x) for nonzero real x less than 1|next=x less than e^x-1 less than x/(1-x) for nonzero real x less than 1}}: 4.2.32 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
Revision as of 20:03, 7 June 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
