高等数学 多元函数微分学，有一个问题就是关于二元函数的极限，是limf（x，y）下面是x趋近于x0
推荐回答（1个）
多元函数的极限是不能累次求的。因为累次求的话，接近的(x0,y0)的路径是没有包含所有可能路径的。
比如f(x,y)=x^2y/(x^4+y^2)
那么lim(x→0)lim(y→0)f(x,y)=lim(y→0)lim(x→0)f(x,y)=0
现在看lim((x,y)→(0,0))f(x,y)
如果沿着y=x接近(0,0)，则f(x,y)→0
如果沿着y=x^2接近(0,0)，则f(x,y)→1/2
所以lim((x,y)→(0,0))f(x,y)不存在
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