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Suppose you have a one variable function which contains an asymptote at a particular point. Is there some sort of phenomenon for two variable functions that is similar to what an asymptote would be for functions of one variable. If there is, what would this phenomenon look like?

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    I am re$f$erring to a somewhat speci$f$ic case. Suppose you have a function in which z=f(y)/g(x) and the limit of that function fails to exist at a point (a,b) because of a somewhat asymptotic quality. In other words, the line x=a is not in the domain of z. What would this look like in three dimensions?2012-03-27

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Perhaps what you have in mind is something like the graph of $z=(x^2+y^2)^{-1}$? Imagine taking the graph of $y=x^{-1}$, the part in the first quadrant, and rotating it around the $y$-axis so you get a surface that looks sort of like a tent held up by a single pole of infinite height. Or find some mathematical graphing software that will do this for you.

EDIT: From the comments, it appears that this is not the kind of thing OP is after. More to the point would be something like $z=x^{-2}$. Now I take it you know what the graph of $y=x^{-2}$ looks like. Take that graph and rotate it through a right angle around the $x$-axis, so that what was the positive $y$-axis is now the positive $z$-axis. Now consider the surface traced out when you move that curve back and forth along the $y$-axis. It sort of looks like two skateboard ramps back-to-back, but each one infinitely high. If my description isn't helping then, as I suggested before, get some software that will graph $z=x^{-2}$ for you.