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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 each case, if the limits of the numerator and denominator are substituted, the resulting expression is /, which is indeterminate. In this sense, 0 / 0 {\displaystyle 0/0} can take on the values 0 {\displaystyle 0} , 1 {\displaystyle 1} , or ∞ {\displaystyle \infty } , by appropriate choices of functions to put in the numerator and denominator.
This is a list of limits for common functions such as elementary functions. In this article, the terms a, b and c are constants with respect to x.
L'Hôpital's rule (/ ˌ l oʊ p iː ˈ t ɑː l /, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives.
The degree of the graph of a rational function is not the degree as defined above: it is the maximum of the degree of the numerator and one plus the degree of the denominator. In some contexts, such as in asymptotic analysis, the degree of a rational function is the difference between the degrees of the numerator and the denominator.
When both the numerator and the denominator tend to zero at the same input, the expression is said to take an indeterminate form, as the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.
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As (+) = and (+) + =, the sum and the product of conjugate expressions do not involve the square root anymore. This property is used for removing a square root from a denominator, by multiplying the numerator and the denominator of a fraction by the conjugate of the denominator (see Rationalisation).