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  2. Implicit function - Wikipedia

    en.wikipedia.org/wiki/Implicit_function

    An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. [ 1 ] : 204–206 For example, the equation x 2 + y 2 − 1 = 0 {\displaystyle x^{2}+y^{2}-1=0} of the unit circle defines y as an implicit function ...

  3. Implicit function theorem - Wikipedia

    en.wikipedia.org/wiki/Implicit_function_theorem

    The unit circle can be specified as the level curve f(x, y) = 1 of the function f(x, y) = x 2 + y 2.Around point A, y can be expressed as a function y(x).In this example this function can be written explicitly as () =; in many cases no such explicit expression exists, but one can still refer to the implicit function y(x).

  4. Implicit curve - Wikipedia

    en.wikipedia.org/wiki/Implicit_curve

    For example, the unit circle is defined by the implicit equation + =. In general, every implicit curve is defined by an equation of the form (,) = for some function F of two variables. Hence an implicit curve can be considered as the set of zeros of a function of two variables

  5. Manifold - Wikipedia

    en.wikipedia.org/wiki/Manifold

    The circle can be represented by a graph in the neighborhood of every point because the left hand side of its defining equation + = has nonzero gradient at every point of the circle. By the implicit function theorem, every submanifold of Euclidean space is locally the graph of a function.

  6. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    The circle of radius ⁠ ⁠ with center at ⁠ (,) ⁠ in the ⁠ ⁠ – ⁠ ⁠ plane can be broken into two semicircles each of which is the graph of a function, ⁠ + ⁠ and ⁠ ⁠, respectively: + = + (), = (), for values of ⁠ ⁠ ranging from ⁠ ⁠ to ⁠ + ⁠.

  7. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). [56]: 204–206 Thus, an implicit function for in the context of the unit circle is defined implicitly by + =.

  8. Dying To Be Free - The Huffington Post

    projects.huffingtonpost.com/dying-to-be-free...

    The last image we have of Patrick Cagey is of his first moments as a free man. He has just walked out of a 30-day drug treatment center in Georgetown, Kentucky, dressed in gym clothes and carrying a Nike duffel bag.

  9. Surface (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Surface_(mathematics)

    Implicit means that the equation defines implicitly one of the variables as a function of the other variables. This is made more exact by the implicit function theorem: if f(x 0, y 0, z 0) = 0, and the partial derivative in z of f is not zero at (x 0, y 0, z 0), then there exists a differentiable function φ(x, y) such that