# Lower bound

by hedipaldi
Tags: bound
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 P: 206 1. The problem statement, all variables and given/known data 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)}? 2. Relevant equations 3. The attempt at a solution I observed that p(x,y) must have even degree.Also if the quotient tend to infinity at the origin the answer is yes.Otherwise p(x,y) must be hogeneous,and this may imly that the quotient has a positive lower bound.I need help for progressing
 Homework Sci Advisor HW Helper Thanks P: 9,921 Have you tried a very simple example, like x^2+y^2?
 P: 206 This is not a counter example.It has a positive lower bound near the origin.
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Lower bound

 Quote by hedipaldi This is not a counter example.It has a positive lower bound near the origin.
... and therefore it is possible. Are you sure the wording of the OP is as you intend?
 P: 206 As i understood,the meaning is to show that for every such p(x,y) there exists such C. How do you understatd the wording?
 P: 206 The original wording is attached:Q.5 Attached Thumbnails
 Homework Sci Advisor HW Helper Thanks P: 9,921 The original wording makes more sense. To express it you should have written "Is it guaranteed that..." If I have any helpful thoughts I'll post again.
 P: 206 Thank's

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