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## Homework Statement

Let p(x,y) be a positive polynomial of degree n ,p(x,y)=0 only at the origin.Is it possible that

the quotient p(x,y)/[absolute value(x)+absval(y)]^n will have a positive lower bound in the punctured rectangle [-1,1]x[-1,1]-{(0,0)}?

## Homework Equations

## The Attempt at a Solution

When the limit at the origin is 0,there is no positive lower bound.If the limit is infinity (which is not seems to be possible) there is such lower bound.This quotient is a special case of rational function in each quadrant,and i try to analyse it.Can someone help?

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