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The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point [1] [2] and exactly one inflection point. Properties
Outside of the range defined by the vertical asymptotes, the inverse function requires computing the logarithm of negative numbers. For this and other reasons it is often impractical to try to fit an inverse Gompertz function to data directly, especially if one only has relatively few data points available from which to calculate the fit.
The section on Slant Asymptote is rather confusing. My math teachers are rather confused looking at it . Can someone who knows a little more about the slant asymptotes both check the math and make it a little easier to understand. --Omnipotence407 14:13, 16 January 2008 (UTC) Much confusion.--( fi ) 23:24, 4 March 2008 (UTC)
The folium of Descartes (green) with asymptote (blue) when = In geometry , the folium of Descartes (from Latin folium ' leaf '; named for René Descartes ) is an algebraic curve defined by the implicit equation x 3 + y 3 − 3 a x y = 0. {\displaystyle x^{3}+y^{3}-3axy=0.}
The field of asymptotics is normally first encountered in school geometry with the introduction of the asymptote, a line to which a curve tends at infinity.The word Ασύμπτωτος (asymptotos) in Greek means non-coincident and puts strong emphasis on the point that approximation does not turn into coincidence.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
Richards's curve has the following form: = + (+) /where = weight, height, size etc., and = time. It has six parameters: : the left horizontal asymptote;: the right horizontal asymptote when =.