1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear oblique asymptote

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    what is the linear oblique asymptote of (x^5+x^3+2)/(x^4-1)
    ?
    2. Relevant equations

    x-a/p(x) = q(x) +remainder

    3. The attempt at a solution

    I put in all the placeholders for the divisor and the numerator and got x as the equation for the linear oblique asymptote?? Is that right??
     
  2. jcsd
  3. Dec 4, 2013 #2

    Mentallic

    User Avatar
    Homework Helper

    We would let

    [tex]\frac{x^5+x^3+2}{x^4-1}\equiv \frac{(ax+b)(x^4-1)+p(x)}{x^4-1} = ax+b + \frac{p(x)}{x^4-1}[/tex]

    Where p(x) is a cubic polynomial or less (doesn't matter what it is exactly).


    If we expanded (ax+b)(x4-1) then we get

    [tex]ax^5+bx^4-ax-b[/tex]

    But we ignore the -ax-b term because that will be a part of p(x) which we've already said we don't care about. So we want the constant a to be chosen such that [itex]ax^5=x^5[/itex] since the coefficient of [itex]x^5[/itex] on the LHS must be equal to the RHS, hence a=1, and b must be chosen such that [itex]bx^4=0[/itex] for the same reason, hence b=0.

    But we ignore the -ax-b term because that will be a part of p(x) which we've already said we don't care about.
     
  4. Dec 4, 2013 #3
    Is the answer that I got correct? Thanks for taking the time to answer. I know how to do it just wondering if it's correct
     

    Attached Files:

  5. Dec 4, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, y= x is the "liner oblique asymptote".
     
  6. Dec 4, 2013 #5

    Mark44

    Staff: Mentor

    No, this isn't correct. It's the equation of the rational function you started with.

    To find the oblique asymptote, either do what Mentallic suggested or carry out the long division to get x + a proper rational function. In a proper rational function, the degree of the numerator is less than that of the denominator.
     
  7. Dec 6, 2013 #6
    Ok thank you
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted