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解ï¼âµlim(x->+â,y->-â)[(x-y)^2/e^(x-y)]
=lim(t->+â)(t^2/e^t) (令t=x-y)
=lim(t->+â)(2t/e^t) (â/âåæéï¼åºç¨ç½æ¯è¾¾æ³å)
=lim(t->+â)(2/e^t) (â/âåæéï¼åºç¨ç½æ¯è¾¾æ³å)
=0
lim(x->+â)(x/e^x)
=lim(x->+â)(1/e^x) (â/âåæéï¼åºç¨ç½æ¯è¾¾æ³å)
=0
lim(y->-â)(ye^y)
=lim(y->-â)[y/e^(-y)]
=lim(y->-â)[-1/e^(-y)] (â/âåæéï¼åºç¨ç½æ¯è¾¾æ³å)
=0
â´lim(x->+â,y->-â)[(x^2+y^2)e^(y-x)]
=lim(x->+â,y->-â)[((x-y)^2-2xy)/e^(x-y)]
=lim(x->+â,y->-â)[(x-y)^2/e^(x-y)-2(x/e^x)(ye^y)]
=lim(x->+â,y->-â)[(x-y)^2/e^(x-y)]-2*lim(x->+â,y->-â)(x/e^x)*lim(x->+â,y->-â)(ye^y)
=0-2*0*0
=0ã
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