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An upperbound for an algebraic expression

bincybn

Member
Apr 29, 2012
36
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

Indicium Physicus
Staff member
Jan 26, 2012
4,197
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.
 

bincybn

Member
Apr 29, 2012
36
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

Indicium Physicus
Staff member
Jan 26, 2012
4,197
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.