An upperbound for an algebraic expression

[bincy]

Hii Everyone,
Plz tell me a tight upperbound for \(\displaystyle \frac{x}{1-x\left(1-y\right)}
\) where o<=x,y<=1

regards,
Bincy

 

[Ackbach]

I don't think there is an upper or lower bound for that function. On the critical curve $x=1/(1-y)$, the function goes to negative infinity, and as, say, $y\to 1/2$ and $x\to 2$, the function goes to positive infinity.

 

[bincy]

I don't think there is an upper or lower bound for that function. On the critical curve $x=1/(1-y)$, the function goes to negative infinity, and as, say, $y\to 1/2$ and $x\to 2$, the function goes to positive infinity.

Plz note that BOTH x and y are in between 0 and 1

 

[Ackbach]

Ah, my mistake. You still have a problem when $y\to 0$ and $x\to 1$. The function blows up there, and there is no upper bound on it.