glossary

asymptotically    

 

A curve is said to approach a straight line asymptotically if the distance between a point P on the curve to the line becomes arbitrarily small as P moves to infinity along some unbounded portion of the curve.

 

Example

The graph of the Cartesian equation xy = 1 is a hyperbola with two asymptotes.

If the equation is written as y = 1/x we see that y approaches 0 as | x | becomes arbitrarily large, so part of the hyperbola approaches the x axis asymptotically.

If the equation is written as x = 1/y we see that x approaches 0 as | y | becomes arbitrarily large, so part of the hyperbola approaches the y axis asymptotically.

 

 
   

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