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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 ...
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.
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 ...
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 ...
Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve. [1] Equate first and second derivatives to 0 to find the stationary points and inflection points respectively. If the equation of the curve cannot be solved explicitly for x or y, finding these derivatives requires implicit ...
Heaviside step function. The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙 ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use.
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 ...
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.