Finding Oblique Asympote by polidiv

  • Thread starter Thread starter BananaJoe
  • Start date Start date
AI Thread Summary
The discussion revolves around determining the existence of oblique asymptotes for functions represented as x^(n+1)/x^n or similar forms. It questions whether a function that perfectly matches another after polynomial division, without any remainder, can still possess oblique asymptotes. The definition of asymptotes is debated, particularly regarding whether a function can be considered an asymptote of itself. Clarification is sought on the mathematical expressions used, as there is confusion about their intended meaning. Overall, the conversation highlights the complexities in defining and identifying oblique asymptotes in mathematical functions.
BananaJoe
Messages
1
Reaction score
0
If you are looking for obli. asympt. for a function where the x^n+1/x^n or any, and you do a polynom division and you get a perfect match wihout any Rests. Does that mean the function doesn't have any obliique asymptotes?
 
Mathematics news on Phys.org
That depends on the definition of asymptote - do you call a function "asymptote" if it is identical to the function you consider?
As in, is g(x)=x+1 an asymptote to f(x)=x+1?
 
BananaJoe said:
If you are looking for obli. asympt. for a function where the x^n+1/x^n or any, and you do a polynom division and you get a perfect match wihout any Rests. Does that mean the function doesn't have any obliique asymptotes?
I'm having a hard time understanding what you're asking.

"where the x^n+1/x^n or any" - what does this mean?
Also, the expression you wrote probably isn't what you meant. What you wrote is this:
xn + 1/xn

I can't tell if you meant ##\frac{x^{n + 1}}{x^n}## or ##\frac{x^n + 1}{x^n}##. Suitably placed parentheses would be a great help.

"perfect match wihout any Rests" - ??
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top