Finding Oblique Asympote by polidiv

  • Thread starter BananaJoe
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In summary, the conversation discusses the concept of oblique asymptotes for a function and whether a function without any remainder after polynomial division is considered to have an oblique asymptote. The definition of an asymptote is also questioned, using the example of g(x)=x+1 being an asymptote to f(x)=x+1. The conversation also clarifies the notation used and asks for further explanation on certain terms.
  • #1
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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?
 
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  • #2
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?
 
  • #3
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" - ??
 

1. What is an oblique asymptote?

An oblique asymptote is a type of asymptote that is not horizontal or vertical, but instead takes on a slanted or diagonal form on a graph.

2. How is an oblique asymptote found using polidiv?

Polidiv, or polynomial long division, is a method used to divide polynomials. When dividing a polynomial function by a linear function, the resulting quotient will be the equation of the oblique asymptote.

3. What is the purpose of finding the oblique asymptote?

The oblique asymptote can help determine the end behavior of a function and provide useful information for graphing the function.

4. Can an oblique asymptote intersect the graph of a function?

Yes, an oblique asymptote can intersect the graph of a function at most once. This intersection point is known as a removable discontinuity.

5. Are there any other methods for finding an oblique asymptote besides polidiv?

Yes, there are other methods such as synthetic division and the use of limits. However, polidiv is typically the most commonly used method in finding oblique asymptotes.

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