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Curved Asymptotes

  1. Feb 20, 2009 #1

    Mentallic

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    Does the definition of an asymptote extend beyond the straight lines?

    In an assignment I stated that for the graph [tex]y=x^2+\frac{1}{x}[/tex] there is an asymptote of [tex]y=x^2[/tex] for x approaching [tex]\pm \infty[/tex]. However, my teacher says that she doesn't believe it to be considered an asymptote.

    So was I right or wrong to make this statement?
     
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  3. Feb 20, 2009 #2

    Gib Z

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  4. Feb 20, 2009 #3
    Your example is the sort of thing commonly seen in asymptotic analysis.

    In computer science you see this a lot. For example if you have 1 program that takes n^2 operations to compute, and another program that takes about n^2 + n operations to compute, then they are considered asymptotically equivalent because for large n, the n^2 term dominates and the +n is basically irrelevant. eg: if n=1000, then the first program takes 1,000,000 operations whereas the second program takes 1,001,000 operations - the runtimes differ by 1/10th of 1 percent.
     
    Last edited: Feb 20, 2009
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