Search results
Results from the WOW.Com Content Network
Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.
for all values of x in the domain. A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental ...
A function that is absolutely monotonic on [,) can be extended to a function that is not only analytic on the real line but is even the restriction of an entire function to the real line. The big Bernshtein theorem : A function f ( x ) {\displaystyle f(x)} that is absolutely monotonic on ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} can be ...
For example, if : [,] is the Dirichlet function that is on irrational numbers and on rational numbers, and [,] is equipped with Lebesgue measure, then the support of is the entire interval [,], but the essential support of is empty, since is equal almost everywhere to the zero function.
The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
Isaac Rosenbloom, 43, doesn’t know whether he has cancer because his insurer won’t approve an MRI for nodules on his lungs, which were found on an X-ray when the Pueblo, Colorado, resident had ...
For z = 1/3, the inverse of the function x = 2 C 1/3 (y) is the Cantor function. That is, y = y ( x ) is the Cantor function. In general, for any z < 1/2, C z ( y ) looks like the Cantor function turned on its side, with the width of the steps getting wider as z approaches zero.