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Math Help - horizontal asymptotes

  1. #1
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    horizontal asymptotes

    Im having a bit of difficulty recalling how to go about this. I remeber that to search for the horizontal asymptotes I would solve to find the limit of x > 0 from the left and right (sice there can only be 2 horizontal asymptotes. Heres the problem below:


    solution:



    I did everything to the point of x-2/(x(x-1)). Why does the x before x-1 mysteriously go away? I started to stray from the solution posted by canceling out the x in x-2 and the first x in the denominator, to get -2/-1 which = 2. What is the difference in procedure in searching for the limit of 0 from the left and the right? Thanks!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    horizontal asymptotes are found in the limit as x-> + infinity.

    In the case of a rational function there can only be one so you only need consider one case.

    In your eg y =0 is the HA as the denominator is of higher degree than the denominator
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