What is meant by Newton's Rules, if A+B=C, A=C and B=C?

[PLAGUE]

TL;DR

Newton's Rules: if A+B=C, A=C and B=C?

What is it meant by Newton's Rules in point (vii)?

 

[pasmith]

Have you looked up "newton's rules" in the index of the text where you found the problem? Certainly google has turned up nothing relevant, which suggests that it is not a currently or widely used term.

Fronthe context, I guess it has something to do with multiple branches at the origin.

 

[Office_Shredder]

I have never heard of this term and couldn't Google it either. I meditated on the technique and I suspect the point is if you're near the origin and x is not equal to y, one of them is smaller, and you can throw out the highest order term in that variable to see locally what the graph looks like. This A+B=C statement is hiding a lot of work if that's what is going on.

 

[PeroK]

There's an asymptotic principle that if $A(x) + B(x) = C(x)$ and both sides tend to infinity, then one of the terms $A(x)$ or $B(x)$ should become negligible towards the limit. So, either $A(x)$ or $B(x)$ is asymptotic to $C(x)$, but probably not both. That is, of course, only a practical rule of thumb.

 

[WWGD]

TL;DR Summary: Newton's Rules: if A+B=C, A=C and B=C?

What is it meant by Newton's Rules in point (vii)?
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Maybe you can paste in a copy of the problem statement and not just the conclusion?

 

[Office_Shredder]

Maybe you can paste in a copy of the problem statement and not just the conclusion?

I think the problem statement is draw a graph of $x^3+y^3=3axy$ but I agree it would have been nice

 

[Gavran]

It is a technique for determining the shape of an algebraic curve close to and far away from the origin. (https://en.wikipedia.org/wiki/Curve_sketching)