(x,y)→(1,1)limy−1xy2−1
To show that the limit does not exist take two different pairs of sequences with limit 1
1, and show that the limit in both cases is not equal.
if we set x = y we get
limy→1y−1y3−1=limy→1(y2+y+1)=3
if we set x = 1 we get
limy→1y−1y2−1=limy→1(y+1)=2
So the limit does not exist.
Answer: the statement that the limit does not exist is true
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