order of vanishing

Definition. Let $x_{0}$ be a zero (http://planetmath.org/ZeroOfAFunction) of the real function $\\Delta$ . The order of vanishing of $\\Delta$ at $x_{0}$ is $n$ , if $\\displaystyle\\lim_{x\\to x_{0}}\\frac{\\Delta(x)}{x^{n}}$ has a non-zero finite value.

Usually, $x_{0}$ of the definition is 0.

Example. If the curves $y=f(x)$ and $y=g(x)$ have in the point $(x_{0},\\,y_{0})$ the order of contact $n$ , then the difference $\\Delta(h):=g(x_{0}+h)-f(x_{0}+h)$ of the ordinates has $n\\!+\\!1$ -order of vanishing.

单词	OrderOfVanishing
释义	order of vanishing Definition. Let $x_{0}$ be a zero (http://planetmath.org/ZeroOfAFunction) of the real function $\\Delta$ . The order of vanishing of $\\Delta$ at $x_{0}$ is $n$ , if $\\displaystyle\\lim_{x\\to x_{0}}\\frac{\\Delta(x)}{x^{n}}$ has a non-zero finite value. Usually, $x_{0}$ of the definition is 0. Example. If the curves $y=f(x)$ and $y=g(x)$ have in the point $(x_{0},\\,y_{0})$ the order of contact $n$ , then the difference $\\Delta(h):=g(x_{0}+h)-f(x_{0}+h)$ of the ordinates has $n\\!+\\!1$ -order of vanishing.
随便看	symmetric multilinear function SymmetricPolynomial symmetric polynomial SymmetricPower symmetric power SymmetricQuarticEquation symmetric quartic equation SymmetricRandomVariable symmetric random variable SymmetricRelation symmetric relation SymmetricSet symmetric set SymmetricTensor symmetric tensor Symmetrizer symmetrizer Symmetry symmetry SymmetryOfAnOrdinaryDifferentialEquation symmetry of an ordinary differential equation SymmetryOfASolutionOfAnOrdinaryDifferentialEquation symmetry of a solution of an ordinary differential equation SymmetryOfDividedDifferences symmetry of divided differences