An oblique asymptote, also called a slant asymptote or tilted asymptote, is a nonhorizontal line 
such that
where 
. For a rational
function, an oblique asymptote occurs when polynomial
division leaves a linear quotient and a remainder
whose ratio to the denominator tends to zero.
See also
Asymptote,
Horizontal Asymptote,
Line,
Rational
Function,
Vertical Asymptote
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References
Apostol, T. M. Calculus,
Vol. 1, 2nd ed. New York: Wiley, 1967.
Cite this as:
Weisstein, Eric W. "Oblique Asymptote."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ObliqueAsymptote.html
Subject classifications
![lim_(x->+/-infty)[f(x)-(mx+b)]=0,](/images/equations/ObliqueAsymptote/NumberedEquation1.svg)
