mean-value theorems

mean-value theorems
In mathematics, two theorems, one associated with differential calculus and one with integral calculus.

The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line connecting the endpoints of the function's graph on that interval. For example, if a car covers a mile from a dead stop in one minute, it must have been traveling exactly a mile a minute at some point along that mile. In integral calculus, the mean value of a function on an interval is, in essence, the arithmetic mean (see mean, median and mode) of its values over the interval. Because the number of values is infinite, a true arithmetic mean is not possible. The theorem shows how to find the mean value using a definite integral. See also Rolle's theorem.

* * *


Universalium. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

  • mean-value theorem — ▪ mathematics       theorem in mathematical analysis dealing with a type of average useful for approximations and for establishing other theorems, such as the fundamental theorem of calculus (analysis).  The theorem states that the slope of a… …   Universalium

  • mean — mean1 /meen/, v., meant, meaning. v.t. 1. to have in mind as one s purpose or intention; intend: I meant to compliment you on your work. 2. to intend for a particular purpose, destination, etc.: They were meant for each other. 3. to intend to… …   Universalium

  • value — /val yooh/, n., v., valued, valuing. n. 1. relative worth, merit, or importance: the value of a college education; the value of a queen in chess. 2. monetary or material worth, as in commerce or trade: This piece of land has greatly increased in… …   Universalium

  • Mean sojourn time — The mean sojourn time for an object in a system is a mathematical term for the amount of time an object is expected to spend in a system before leaving the system for good. Contents 1 Explanation 2 Calculation 3 See also 4 References …   Wikipedia

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • Bounded mean oscillation — In harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real valued function whose mean oscillation is bounded (finite). The space of functions of bounded mean oscillation (BMO), is a function space that,… …   Wikipedia

  • Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia

  • Mertens' theorems — For Mertens theorem on convergence of Cauchy products of series, see Cauchy product#Convergence and Mertens.27 theorem. In number theory, Mertens theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens… …   Wikipedia

  • Abelian and tauberian theorems — In mathematics, abelian and tauberian theorems relate to the meaningful assignment of a value as the sum of a class of divergent series. A large number of methods have been proposed for the summation of such series, generally taking the form of… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”