Asymptote
Oblique asymptotes

When a linear asymptote is not parallel to the x - or y -axis, it is called an oblique asymptote or slant asymptote. A function ƒ (x) is asymptotic to the straight line y = mx + n (m ≠ 0) if

In the first case the line y = mx + n is an oblique asymptote of ƒ (x) when x tends to +∞, and in the second case the line y = mx + n is an oblique asymptote of ƒ (x) when x tends to − ∞.

An example is ƒ (x) = x + 1/ x, which has the oblique asymptote y = x (that is m = 1, n = 0) as seen in the limits
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