Vipul: Created page with "==Definition== ===For a curve=== {{fillin}} ===For a function=== Suppose $f$ is a function whose domain contains an interval of the form $(a,\infty)$ fo..."

2011-09-19T23:48:27Z

Created page with "==Definition== ===For a curve=== {{fillin}} ===For a function=== Suppose <math>f</math> is a function whose domain contains an interval of the form <matH>(a,\infty)</math> fo..."

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==Definition==

===For a curve===

{{fillin}}

===For a function===

Suppose <math>f</math> is a function whose domain contains an interval of the form <matH>(a,\infty)</math> for some real number <math>a</math> or an interval of the form <math>(-\infty,b)</math> for some real number <math>b</math>. We say that the line <math>y = L</math> is a '''horizontal asymptote''' for the [[graph]] of <math>f</math> if '''one or both of these holds''':

<math>\! \lim_{x \to \infty} f(x) = L, \qquad \lim_{x \to -\infty} f(x) = L</math>

==Related notions==

* [[Vertical asymptote]]
* [[Oblique asymptote]]
* [[Additively asymptotic functions]]
* [[Multiplicatively asymptotic functions]]

Horizontal asymptote - Revision history

Vipul: Created page with "==Definition== ===For a curve=== {{fillin}} ===For a function=== Suppose f is a function whose domain contains an interval of the form (a,\infty) fo..."

Vipul: Created page with "==Definition== ===For a curve=== {{fillin}} ===For a function=== Suppose $f$ is a function whose domain contains an interval of the form $(a,\infty)$ fo..."