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implicit function theorem |
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implicit function theorem [im′plis·ət ¦fəŋk·shən ‚thir·əm]
(mathematics) A theorem that gives conditions under which an equation in variablesxandymay be solved so as to expressydirectly as a function ofx; it states that ifF(x,y) and ∂F(x,y)/∂yare continuous in a neighborhood of the point (x0,y0) and ifF(x,y) = 0 and ∂F(x,y)/∂y≠ 0, then there is a number ε > 0 such that there is one and only one function ƒf(x) that is continuous and satisfiesF[x,ƒ(x)] = 0 for |x-x0| < ε, and satisfies ƒ(x0) =y0. Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content. |
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