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  2. Conchoid of de Sluze - Wikipedia

    en.wikipedia.org/wiki/Conchoid_of_de_Sluze

    The point most distant from the asymptote is (1 + a, 0). (0,0) is a crunode for a < −1 . The area between the curve and the asymptote is, for a ≥ −1 ,

  3. Asymptotic analysis - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_analysis

    In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large.

  4. Asymptotology - Wikipedia

    en.wikipedia.org/wiki/Asymptotology

    In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. . Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and phy

  5. Asymptotic curve - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_curve

    The asymptotic directions are the same as the asymptotes of the hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic point. [1] An asymptotic direction is a direction along which the normal curvature is zero: take the plane spanned by the direction and the surface's normal at that point. The ...

  6. Asymptote - Wikipedia

    en.wikipedia.org/wiki/Asymptote

    Asymptotes are used in procedures of curve sketching. An asymptote serves as a guide line to show the behavior of the curve towards infinity. [10] In order to get better approximations of the curve, curvilinear asymptotes have also been used [11] although the term asymptotic curve seems to be preferred. [12]

  7. Tractrix - Wikipedia

    en.wikipedia.org/wiki/Tractrix

    The arc length of one branch between x = x 1 and x = x 2 is a ln ⁠ y 1 / y 2 ⁠. The area between the tractrix and its asymptote is ⁠ π a 2 / 2 ⁠, which can be found using integration or Mamikon's theorem. The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a ...

  8. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    A sigmoid function is constrained by a pair of horizontal asymptotes as . A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0.

  9. Strophoid - Wikipedia

    en.wikipedia.org/wiki/Strophoid

    Print/export Download as PDF; Printable version; In other projects ... (0, 0) and the line y = b is an asymptote. The right strophoid