Editing Asymptote (section)

===Oblique asymptotes===
[[File:1-over-x-plus-x.svg|right|thumb|220px|In the graph of <math>f(x) = x+\tfrac{1}{x}</math>, the ''y''-axis (''x'' = 0) and the line ''y'' = ''x'' are both 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 {{nowrap|1=''y'' = ''mx'' + ''n''}} (''m''&nbsp;≠&nbsp;0) if

:<math>\lim_{x \to +\infty}\left[ f(x)-(mx+n)\right] = 0 \, \mbox{ or } \lim_{x \to -\infty}\left[ f(x)-(mx+n)\right] = 0.</math>

In the first case the line {{nowrap|1=''y'' = ''mx'' + ''n''}} is an oblique asymptote of ''ƒ''(''x'') when ''x'' tends to +∞, and in the second case the line {{nowrap|1=''y'' = ''mx'' + ''n''}} is an oblique asymptote of ''ƒ''(''x'') when ''x'' tends to &minus;∞.

An example is ''ƒ''(''x'')&nbsp;=&nbsp;''x'' + 1/''x'', which has the oblique asymptote ''y''&nbsp;=&nbsp;''x'' (that is ''m''&nbsp;=&nbsp;1, ''n''&nbsp;=&nbsp;0) as seen in the limits
:<math>\lim_{x\to\pm\infty}\left[f(x)-x\right]</math>
:<math>=\lim_{x\to\pm\infty}\left[\left(x+\frac{1}{x}\right)-x\right]</math>
:<math>=\lim_{x\to\pm\infty}\frac{1}{x}=0.</math>