(x^2*(y-1)^2)/(x^2+(y-1)^2) for (x,y) at (0,1)

Question

David · Accepted Answer

We wish to evaluate the following limit:
 
   
 
 
22
22, 0,1
1
lim .
1x y
x y
L
x y
 
  
   

We claim that 0.L   To see this, we must show that for all 0,   there exists 0   such that if 
 
22 1x y     then
 
 
 
22
22
1
.

(x^2*(y-1)^2)/(x^2+(y-1)^2) for (x,y) at (0,1)

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