CALCULUS Understanding Its Concepts and Methods

Asymptotes

The vertical line *x* = *a* is a vertical asymptote of the function *f* if the limit of *f*(*x*) as *x*
goes to *a* from the
right or from the left is equal to
or .
To say that the limit of *f*
(*x*) as *x* goes to *a* from the right is
equal to ∞, which is written asmeans
that the values of *f*(*x*) become arbitrarily large
if *x* is sufficiently
close to, but greater than, the number *a*.

The horizontal line *y* = * c*
is a horizontal asymptote of the
function *f * if
the limit of *f*(*x*) as *x* goes to
or
is equal to *c*.

vertical
asymptote |
horizontal
asymptote |

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.