Oblique AsymptoteDate: 4/13/96 at 23:46:53 From: Mohammad Mehdi Moshfeghian Subject: Asymptotes Dear Dr Math. I have a question about the oblique asymptote of the function F( X ) = ( X^3 - 3X^2 + 2X - 8 ) / ( X^2 + 4X + 4 ). According to the graph the line Y = X - 7 is the asymptote but it crosses the F ( X ) at about X = - 0. 769 I assumed that the asymptotes would not cross the functions. I would appreciate any help with this problem. Regards, M.M.Moshfeghian Date: 6/28/96 at 14:10:10 From: Doctor Jerry Subject: Re: Asymptotes If X^3 - 3X^2 + 2X - 8 is divided by X^2 + 4X + 4, the result is ( X^3 - 3X^2 + 2X - 8 ) / ( X^2 + 4X + 4 ) = X-7 + (26X+20)/(X^2+4X+4). From this it is possible to see that the limit of F(X) as X increases without bound is X-7. If X = 10,000,000, for example, the fraction (26X+20)/(X^2+4X+4) is 2.6 times 10^(-6). So F(X) becomes and remains close to G(X) = X-7. The important thing about one curve being an asymptote of another is how the curves behave as X increases without bound. Often, curves do not cross their asymptotes, but this is not a requirement. -Doctor Jerry, The Math Forum |
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