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*edit* oops sorry, I meant to post this in homework help

- Thread starter Esoremada
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- #1

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*edit* oops sorry, I meant to post this in homework help

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Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches. Under this definition, a line has no asymptotes.

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pwsnafu

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Except functions like ##\frac{\sin x}{x}## cross their asymptote an infinite number of times.Asymptotes are usually defined as lines that a given function approaches infinitely close, but never reaches.

Formal definition from Wikipedia:

This is really iffy. You could argue either way.Let ##A:(a,b)\rightarrow\mathbb{R}^2## be a parametric curve, in coordinates ##A(t)=(x(t),y(t))##. Suppose the curve tends to infinity, that is:

##\lim_{t\rightarrow b}(x^2(t)+y^2(t))=\infty##.

A line ##\mathcal{l}## is an asymptote of A if the distance from A(t) to ##\mathcal{l}## tends to zero as ##t\rightarrow b##

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