推 playmypig :謝謝您詳細的解答啊 10/29 00:10
:用e-d極限定義證明y=(x+1)^3在R連續
:求教了, 不懂找出delta來呢:(
y=f(x)=(x+1)^3
continuous: lim [f(x+h) - f(x)] = 0
h->0
∵h->0 ∴consider -1≦h≦1
|(x+1+h)^3-(x+1)^3| ≦ |3h(x+1)^2| + |3h^2(x+1)| + |h^3|
≦ |3(x+1)^2|*|h| + |3(x+1)|*|h| + |h|
≦ M*|h|, where M = 3*Max(|3(x+1)^2|,|3(x+1)|,1)
∴Given ε>0 , let δ=min(1,ε/M)
then |h|<δ implies |(x+1+h)^3-(x+1)^3|<ε
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