If this limit doesn't exist then there is no oblique asymptote in that direction.
From the en.wikipedia.org
The integral may fail to exist because of a vertical asymptote in the function.
From the en.wikipedia.org
The asymptote is the polynomial term after dividing the numerator and denominator.
From the en.wikipedia.org
Only open curves that have some infinite branch, can have an asymptote.
From the en.wikipedia.org
The notion of asymptote is related to procedures of curve sketching.
From the en.wikipedia.org
Asia and the world do not asymptote within the range shown.
From the nature.com
An asymptote serves as a guide line that serves to show the behavior of the curve towards infinity.
From the en.wikipedia.org
A central conic is called an ellipse or a hyperbola according as it has no asymptote or two asymptotes.
From the en.wikipedia.org
Therefore the understanding of the idea of an asymptote requires an effort of reason rather than experience.
From the en.wikipedia.org
More examples
A straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. ...
Asymptote is a New York-based architectural office founded in 1989 by principals Hani Rashid and Lise Anne Couture.
Asymptote is a descriptive vector graphics language, developed by Andy Hammerlindl, John C. Bowman (University of Alberta), and Tom Prince, that provides a natural coordinate-based framework for technical drawing. Asymptote runs on all major platforms (UNIX, Mac OS, Microsoft Windows). ...
(Asymptotes) Straight lines that have the property of becoming and staying arbitrarily close to the curve as the distance from the origin increases to infinity. For example, the x- axis is the only asymptote to the graph of sin( x)/x.
The asymptote of a function as it is now used is a much narrower definition than the original Greek meaning. The word joins the roots a (not), with sum (together) + piptein (to fall) and literally means "not falling together", or not meeting. ...
An asymptote is like one of those people you meet at a party who is devastatingly attractive and you just want to get close. You maneuver your way next to them and casually strike up a conversation. Making good time, you get closer and closer, till you're practically knocking knees. ...
The upper or lower bound to a relationship that is approached continuously, but never reached. Photosynthetic response curves approach Amax asymptotically.
In coordinate geometry, a straight line that a curve approaches more and more closely but never reaches. The x and y axes are asymptotes to the graph of xy = constant (a rectangular hyperbola). ...