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Then an equation expressing y as an implicit function of the other variables can be written. The defining equation R(x, y) = 0 can also have other pathologies. For example, the equation x = 0 does not imply a function f(x) giving solutions for y at all; it is a vertical line.
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).
Implicit means that the equation is not expressed as a solution for either x in terms of y or vice versa. If F ( x , y ) {\displaystyle F(x,y)} is a polynomial in two variables, the corresponding curve is called an algebraic curve , and specific methods are available for studying it.
In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form y 2 − a 2 x 3 = 0 {\displaystyle y^{2}-a^{2}x^{3}=0} (with a ≠ 0 ) in some Cartesian coordinate system .
Circular reference in worksheets can be a very useful technique for solving implicit equations such as the Colebrook equation and many others, which might otherwise require tedious Newton-Raphson algorithms in VBA or use of macros. [4]
Implicit function: defined implicitly by a relation between the argument(s) and the value. Piecewise function: is defined by different expressions on different intervals. Computable function: an algorithm can do the job of the function. Also semicomputable function; primitive recursive function; partial recursive function.
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