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

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Newton's Rules: if A+B=C, A=C and B=C?
What is it meant by Newton's Rules in point (vii)?
Screenshot 2024-02-21 141024.png
Screenshot 2024-02-21 141049.png
 
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  • #2
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.
 
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  • #3
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.
 
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  • #4
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.
 
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  • #5
PLAGUE said:
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)?
View attachment 340639View attachment 340641
Maybe you can paste in a copy of the problem statement and not just the conclusion?
 
  • #6
WWGD said:
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
 
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