一道高数题,求二元函数的极限求lim(x^2+y^2)e^(-x-y),条件（x,y）趋向（无穷大,无穷大）无穷大指的是正无穷大。答案是0

Question

一道高数题,求二元函数的极限
求lim(x^2+y^2)e^(-x-y),条件（x,y）趋向（无穷大,无穷大）
无穷大指的是正无穷大。答案是0

Answer 1

lim(x->无穷,y->无穷）（x^2+y^2)e^（-x-y)
=lim(x->无穷,y->无穷）[x^2*e^(-x)*e^(-y)+y^2*e^(-x)*e^(-y)]
=lim(x->无穷)x^2*e^(-x)]*lim(y->无穷）e^(-y)
+lim(y->无穷）y^2*e^(-y)*lim(x->无穷）e^(-x)
=0