单词 | implicit function theorem |
释义 | implicit function theorem [im`plis·ǝt ¦fǝŋk·shǝn ´thir·ǝm] MATHEMATICS A theorem that gives conditions under which an equation in variables x and y may be solved so as to express y directly as a function of x; it states that if F (x,y ) and ∂F (x,y )/∂y are continuous in a neighborhood of the point (x0,y0) and if F (x,y ) = 0 and ∂F (x,y )/∂y ≠ 0, then there is a number ∊ > 0 such that there is one and only one function f (x ) that is continuous and satisfies F[x, f (x )] = 0 for |x - x0| < ∊, and satisfies f (x0) = y0. |
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