1: 2016-11-02 (水) 01:21:35 osinko  |
2: 2016-11-02 (水) 02:04:58 osinko |
| | TITLE:イプシロンデルタ_メモ | | TITLE:イプシロンデルタ_メモ |
| | #jsmath | | #jsmath |
| | + | |
| | + | **メモ [#gdcfd268] |
| | + | \(\lim _{ n\rightarrow \infty }{ { a }_{ n } } =\alpha \\ \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad \left| { a }_{ n }-\alpha \right| <\varepsilon \quad )\\ \quad \Leftrightarrow \quad \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad \alpha -\varepsilon <{ a }_{ n }<\alpha +\varepsilon \quad )\) |
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| | + | \( \lim _{ n\rightarrow \infty }{ \frac { 1 }{ n } } =0\\ \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad 0-\varepsilon <\frac { 1 }{ n } <0+\varepsilon \quad )\) |
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| | + | \( \lim _{ n\rightarrow \infty }{ \frac { 1 }{ n } } +3=3\\ \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad \left| \frac { 1 }{ n } +3-3 \right| <\varepsilon \quad )\\ \quad \Leftrightarrow \quad \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad 3-\varepsilon <\frac { 1 }{ n } +3<3+\varepsilon \quad )\\ \quad \Leftrightarrow \quad \forall \varepsilon >0\quad \exists \delta >0\quad \forall n\in { N }\quad (\quad n>\delta \quad \Rightarrow \quad 0-\varepsilon <\frac { 1 }{ n } <0+\varepsilon \quad )\) |
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| | + | \( \lim _{ x\rightarrow a }{ f\left( x \right) } =\alpha \) |
| | + | \( \forall \varepsilon >0\quad \exists \delta >0\quad (\quad \delta >\left| x-a \right| >0\quad \Rightarrow \quad \left| f\left( x \right) -\alpha \right| <\varepsilon \quad )\\ \quad \Leftrightarrow \quad \forall \varepsilon >0\quad \exists \delta >0\quad ((a-\delta <x<a+\delta \quad \wedge \quad x≠a)\quad \Rightarrow \quad \alpha -\varepsilon <f\left( x \right) <\alpha +\varepsilon \quad ) \) |
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| | + | \( \lim _{ x\rightarrow 1 }{ \frac { 1 }{ x } } +2=3 \) |
![[PukiWiki]](http://unitylabo.s601.xrea.com/xoops/modules/xpwiki/image/pukiwiki.png "[PukiWiki]")
