[分析]偏導數

[rebe212296 (綠豆冰)]

f(x,y)= (2xy)/(x^2+y^2) for all (x,y)≠(0,0)

Determine the existence of the limt

解:

lim lim  (2xy)/(x^2+y^2)=0
x→0 y→0

lim lim  (2xy)/(x^2+y^2)=0
y→0 x→0

Along y=x lim(2y^2)/(2y^2)=1
          y→0

the double limit doesn't exist.


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