作者SMer (奈落之夜‧宵)
看板trans_math
标题Re: [多变] 一题极限证明
时间Sat Mar 10 10:02:54 2007
※ 引述《pobm (待从头收拾旧河山)》之铭言：
: (x^2)y
: lim ------------- =0
: (x,y)→(0,0) (x^2)+(y^2)
: 请用δ-ε证明
: 谢谢^^
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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1F：推 pobm:谢谢^^125.228.181.164 03/12 12:21