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?
Asymptotic qualities but in three dimentions
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calculus
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0Interesting question. Sorry, but my comment is nothing more than a comment. – 2012-03-27
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0But for what it's worth, I imagine it would look like a black hole. – 2012-03-27
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0An analogue would be if there is a plane $\pi$ such that when $x$ and $y$ are large, the point $(x,y,f(x,y))$ is close to $\pi$. – 2012-03-27
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0And what, emiller, does a black hole look like? – 2012-03-27
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0I am referring to a somewhat specific 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