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Mathematics · 术语表

什么是 Asymptotes?

又称: asymptote

Definition 21.4 High School Mathematics · 第 21 章 — Limits and Continuity

The line y=ℓy = \ell is a horizontal asymptote of the curve of ff at +∞+\infty (resp. −∞-\infty) if lim⁡x→+∞f(x)=ℓ\lim_{x\to+\infty} f(x) = \ell (resp. at −∞-\infty). The line x=ax = a is a vertical asymptote if ff has an infinite one-sided limit at aa.

The curve of f(x) = 2 + 1/x-1 with its horizontal asymptote y = 2 (at ±∈fty) and vertical asymptote x = 1.
The curve of f(x)=2+1x−1f(x) = 2 + \frac{1}{x-1} with its horizontal asymptote y=2y = 2 (at ±∞\pm\infty) and vertical asymptote x=1x = 1.
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