Does anyone know of any real-world situations (in science, engineering, etc) where a parabolic (or otherwise curvilinear) asymptote comes into relevance?
Thanks...
Here's one: when a string hangs under its own weight it forms a catenery, which is a constant times the hyperbolic cosine: $\displaystyle y = \frac A 2 (e^x + e^{-x})$. For large values of x this assymptotically approaches $\displaystyle y = \frac A 2 e^x $.
Also, I've found several websites that present it this way:
$\displaystyle y = \frac{A}{2} \left( e^{x/a} + e^{-x/a} \right) $
Is this what you meant, or is this something different?