Slant/Oblique Asymptotes in Terms of Limits - Expii

A function f(x) has a slant/oblique asymptote y=mx+b if and only if the difference between the function f(x) and the asymptote mx+b has a limit of 0 as x approaches infinity (or negative infinity). A horizontal asymptote is the same as a slant asymptote with slope m=0.