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If a curve is arbitrarily close to an infinite segment of a line L, then L is called an asymptote of the curve. Equivalently, we give the following: Definition: The line y = mx + c (m ≠ 0) is called an asymptote of a curve y = ƒ(x) if the perpendicular distance of any point P(x, y) on the curve from the line approaches zero as x ∞ + or - ∞. We shall now determine the conditions in order that the line y = mx + c is an asymptote of the curve y = ƒ(x). If p denotes the perpendicular distance of any point P(x, y) on the curve from the line, then By definition p 0 as x ± ∞ (y – mx – c) = 0 (i) Since otherwise the limit in (ii) would be This determines the value of m. Now, by (i), we have c = m (y – mx) (iv) This determines the value of c. Rule: The line y = mx + c (m ≠ 0) is an asymptote of the curve y = ƒ(x), where m and c are determined by m y/x ,c = (y – mx). Services: - Asymptotes Homework | Asymptotes Homework Help | Asymptotes Homework Help Services | Live Asymptotes Homework Help | Asymptotes Homework Tutors | Online Asymptotes Homework Help | Asymptotes Tutors | Online Asymptotes Tutors | Asymptotes Homework Services | Asymptotes