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? asked in 教育與參考考試 · 1 decade ago

極限的證明問題,請你用定義ε,δ論證的方法

Use the definition of the limit to prove that lim x->0 (5x^2 - 4)=-4

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  • 1 decade ago
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    Use the definition of the limit to prove that lim x->0 (5x2 - 4)=-4

    我們先分析一下, |5x2-4-(-4)|<ε ⇒5|x2|<ε所以|x|<ε/5

    0<|x-0|<δ⇒0<|x2|<δ2<δ<1

    Proof: For all ε>0, we take δ=min{1,ε/5}, x belongs to domain of f and 0<|x-0|<δ, |5x2-4-(-4)|=5|x2|<5δ2<5δ<5.ε/5

    This proves

    lim (5x2 - 4)=- 4

    x->0

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