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  2. Asymptote - Wikipedia

    en.wikipedia.org/wiki/Asymptote

    Asymptote. The graph of a function with a horizontal ( y = 0), vertical ( x = 0), and oblique asymptote (purple line, given by y = 2 x ). A curve intersecting an asymptote infinitely many times. In analytic geometry, an asymptote ( / ˈæsɪmptoʊt /) of a curve is a line such that the distance between the curve and the line approaches zero as ...

  3. Asymptotic analysis - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_analysis

    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. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared ...

  4. Truncus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Truncus_(mathematics)

    Truncus (mathematics) In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points ( x, y) satisfying an equation of the form. A mathematical graph of the basic truncus formula, marked in blue, with domain and range both restricted to [-5, 5]. where a , b, and c are given constants.

  5. Method of matched asymptotic expansions - Wikipedia

    en.wikipedia.org/wiki/Method_of_matched...

    Method of matched asymptotic expansions. In mathematics, the method of matched asymptotic expansions [1] is a common approach to finding an accurate approximation to the solution to an equation, or system of equations. It is particularly used when solving singularly perturbed differential equations. It involves finding several different ...

  6. Tractrix - Wikipedia

    en.wikipedia.org/wiki/Tractrix

    The function admits a horizontal asymptote. The curve is symmetrical with respect to the y-axis. The curvature radius is r = a cot ⁠ x / y ⁠. A great implication that the tractrix had was the study of its surface of revolution about its asymptote: the pseudosphere.

  7. Folium of Descartes - Wikipedia

    en.wikipedia.org/wiki/Folium_of_Descartes

    The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting. In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes which is ...

  8. Asymptotic expansion - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_expansion

    Asymptotic expansion. In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular ...

  9. Gompertz function - Wikipedia

    en.wikipedia.org/wiki/Gompertz_function

    The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the ...

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