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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 ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve . A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: [ 1] Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of ...
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 ...
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log ( x ) (blue). In science and engineering, a semi-log plot / graph or semi-logarithmic plot / graph has one axis on a logarithmic scale, the other on a linear scale.
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 ...
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 ...
Definition. The Bode plot for a linear, time-invariant system with transfer function ( being the complex frequency in the Laplace domain) consists of a magnitude plot and a phase plot. The Bode magnitude plot is the graph of the function of frequency (with being the imaginary unit ). The -axis of the magnitude plot is logarithmic and the ...
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient ...