Curved Asymptotes: Is the Definition Extended Beyond Straight Lines?

[Mentallic]

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

In an assignment I stated that for the graph $$y=x^2+\frac{1}{x}$$ there is an asymptote of $$y=x^2$$ for x approaching $$\pm \infty$$. 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?

 

[Gib Z]

Look up the definition: http://en.wikipedia.org/wiki/Asymptote

You are correct.

 

[maze]

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.