Re: [多變] 一題極限證明

[SMer (奈落之夜‧宵)]

※ 引述《pobm (待從頭收拾舊河山)》之銘言：
:                 (x^2)y
:      lim     ------------- =0
: (x,y)→(0,0)  (x^2)+(y^2)
: 請用δ-ε證明
: 謝謝^^

Put f(x,y) = (yx^2)/[(x^2) + (y^2)]

Given any e>0, there is d = e so that

|f(x,y) - 0|

= |(yx^2)/[(x^2) + (y^2)]|

≦ |(y[(x^2) + (y^2)])/[(x^2) + (y^2)]|

= |y|

≦ √(x^2 + y^2)

< e whenever 0 < |(x,y) - (0,0)| = √(x^2 + y^2) < d

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推 pobm:謝謝^^