
#1
Dec2412, 05:59 PM

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 



#2
Dec2512, 05:27 AM

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,172

Have you tried a very simple example, like x^2+y^2?




#3
Dec2512, 06:05 AM

P: 206

This is not a counter example.It has a positive lower bound near the origin.




#4
Dec2512, 06:26 PM

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,172

Lower bound 



#5
Dec2512, 06:34 PM

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? 



#6
Dec2512, 06:58 PM

P: 206

The original wording is attached:Q.5




#7
Dec2512, 11:31 PM

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,172

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. 



#8
Dec2612, 07:41 AM

P: 206

Thank's



Register to reply 
Related Discussions  
greatest lower bound/least upper bound in Q  Calculus  1  
Least upper bound/ greatest lower bound proof  Calculus & Beyond Homework  4  
Upper bound and lower bound  Calculus & Beyond Homework  1  
How do we find the least upper bound and greatest lower bound?  Calculus & Beyond Homework  2  
Upper bound/Lower Bound  Set Theory, Logic, Probability, Statistics  10 