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In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that ...
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
The consumer, however, may violate this logical assumption and purchase product C regardless of the availability of the preferred others when there is no way to rationalize the purchase of A or B instead of C. [9] As rationalization is associated with the decision making the process more so than the decision itself, the explanation for this ...
Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function , whose graph is a hyperbola, and whose domain is the whole real line except for 0.
The rational function defined by the quotient of two homogeneous polynomials is a homogeneous function; its degree is the difference of the degrees of the numerator and the denominator; its cone of definition is the linear cone of the points where the value of denominator is not zero.
Rationalization (sociology), the replacement of traditions, values, and emotions as motives for behavior in society with rational motives; Rationalization, appropriate placement of a factor such as was done with 4π for Heaviside–Lorentz units
For a function whose values grow without bound, the function diverges and the usual limit does not exist. However, in this case one may introduce limits with infinite values. Let f : S → R {\displaystyle f:S\to \mathbb {R} } be a function defined on S ⊆ R . {\displaystyle S\subseteq \mathbb {R} .}
Every rational function is meromorphic on the whole Riemann sphere, and, in this case, the sum of orders of the zeros or of the poles is the maximum of the degrees of the numerator and the denominator.