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Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that
Mean_value_theorem
In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers. It is an important inequality in analytic number
Vinogradov's mean-value theorem
Vinogradov's_mean-value_theorem
In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. For any n + 1 pairwise
Mean value theorem (divided differences)
Mean_value_theorem_(divided_differences)
Theorem in real analysis
derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem. If a real function
Rolle's_theorem
Relationship between derivatives and integrals
dt.} By the first part of the theorem, we know G is also an antiderivative of f. Since F′ − G′ = 0 the mean value theorem implies that F − G is a constant
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Study of rates of change
those endpoints it has a horizontal tangent line. The mean value theorem generalizes Rolle's theorem. If a function is continuous on a closed interval [
Differential_calculus
Approximation of a function by a polynomial
Taylor's theorem are usually proved using the mean value theorem, whence the name. Additionally, notice that this is precisely the mean value theorem when
Taylor's_theorem
Operation in differential calculus
arithmetic mean of the left and right derivatives at that point, if the latter two both exist. Neither Rolle's theorem nor the mean-value theorem hold for
Symmetric_derivative
Difference of two numbers divided by the logarithm of their quotient
\over (t+x)\,(t+y)}.} One can generalize the mean to n + 1 variables by considering the mean value theorem for divided differences for the n-th derivative
Logarithmic_mean
Mathematical theorem in complex analysis
necessarily has value 0) at an isolated zero of f ( z ) {\displaystyle f(z)} . Another proof works by using Gauss's mean value theorem to "force" all points
Maximum_modulus_principle
All derivatives have the intermediate value property
analysis, Darboux's theorem states that the derivative of any real-valued function of a real variable has the intermediate value property, that is, that
Darboux's_theorem_(analysis)
Formula for the average value of a function over its domain
calculus, the mean of a function is loosely defined as the average value of the function over its domain. In a one-dimensional domain, the mean f ¯ {\displaystyle
Mean_of_a_function
Continuous function on an interval takes on every value between its values at the ends
In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval
Intermediate_value_theorem
Topics referred to by the same term
Cauchy theorem may refer to: Cauchy's integral theorem in complex analysis, also Cauchy's integral formula Cauchy's mean value theorem in real analysis
Cauchy_theorem
Theorem in mathematics
}(0)=I} , so that a = b = 0 {\displaystyle a=b=0} . By the mean value theorem for vector-valued functions, for a differentiable function u : [ 0 , 1 ] →
Inverse_function_theorem
Chinese-American mathematician
multivariable generalization of the central conjecture in Vinogradov's mean-value theorem. Zhang was awarded the 2023 SASTRA Ramanujan Prize for his contributions
Ruixiang_Zhang
Theory of speed in physics
The mean speed theorem, also known as the Merton rule of uniform acceleration, was discovered in the 14th century by the Oxford Calculators of Merton College
Mean_speed_theorem
Functions in mathematics
including the mean value theorem (over geodesic balls), the maximum principle, and the Harnack inequality. With the exception of the mean value theorem, these
Harmonic_function
Mathematics of real numbers and real functions
establishes the main theorems about the derivative, such as the mean value theorem and some of its generalizations like the Cauchy mean value theorem. Roughly speaking
Real_analysis
Mathematical rule for evaluating limits
interval is grandfathered in from the hypothesis of the Cauchy's mean value theorem. The notable exception of the possibility of the functions being not
L'Hôpital's_rule
Mathematical theorem
Conversely, instead of using the generalized mean value theorem in the second proof, the classical mean valued theorem could be used. The properties of repeated
Symmetry of second derivatives
Symmetry_of_second_derivatives
is a consequence of the Hahn-Banach theorem and generalizes the mean value theorem for integrals of real-valued functions: If V = R {\displaystyle V=\mathbb
Pettis_integral
Number taken as representative of a list of numbers
Central limit theorem Central moment Descriptive statistics Expected value Kurtosis Law of averages Location parameter Mean value theorem Moment (mathematics)
Average
Square root of the mean square
In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle
Root_mean_square
Differentiation under the integral sign formula
convergence theorem and the mean value theorem (details below). We first prove the case of constant limits of integration a and b. We use Fubini's theorem to change
Leibniz_integral_rule
Definite integral of a scalar or vector field along a path
s_{i}\to 0}\sum _{i=1}^{n}f(\mathbf {r} (t_{i}))\,\Delta s_{i}.} By the mean value theorem, the distance between subsequent points on the curve, is Δ s i = |
Line_integral
Topics referred to by the same term
four-square theorem, which states that every positive integer can be expressed as the sum of four squares of integers Mean value theorem in calculus The
Lagrange's_theorem
Class of partial differential equations
particular, the ultrahyperbolic equation satisfies an analog of the mean value theorem for harmonic functions. Ismael Herrera; George F. Pinder. "APPENDIX
Ultrahyperbolic_equation
Fundamental theorem in probability theory and statistics
the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard
Central_limit_theorem
On when a family of real, continuous functions has a uniformly convergent subsequence
the result. A further generalization of the theorem was proven by Fréchet (1906), to sets of real-valued continuous functions with domain a compact metric
Arzelà–Ascoli_theorem
Conjecture on zeros of the zeta function
been enlarged by several authors using methods such as Vinogradov's mean-value theorem. The most recent paper by Mossinghoff, Trudgian and Yang is from December
Riemann_hypothesis
Unsolved mathematical problem
The mean value problem is an open problem in the mathematical field of complex analysis first posed by Stephen Smale in 1981. The problem asks: For a given
Mean_value_problem
Theorem in vector calculus
Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of
Stokes'_theorem
Conditions for switching order of integration in calculus
slices, the value of a double integral does not depend on the order of integration when the hypotheses of the theorem are satisfied. The theorem is named
Fubini's_theorem
value theorem Differential equation Differential operator Newton's method Taylor's theorem L'Hôpital's rule General Leibniz rule Mean value theorem Logarithmic
List_of_calculus_topics
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Japanese mathematician (1905–1948)
on initial value problems of ordinary differential equations for the solution to be unique. He also refined the second mean value theorem of integration
Hiroshi_Okamura
Indefinite integral
[x_{i-1},x_{i}]} as specified by the mean value theorem, then the corresponding Riemann sum telescopes to the value F ( b ) − F ( a ) {\displaystyle F(b)-F(a)}
Antiderivative
Type of metric geometry
s_{i}=\Delta x_{i}+\Delta y_{i}=\Delta x_{i}+|f(x_{i})-f(x_{i-1})|.} By the mean value theorem, there exists some point x i ∗ {\displaystyle x_{i}^{*}} between x
Taxicab_geometry
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Method for assigning values to integrals
meromorphic, the Sokhotski–Plemelj theorem relates the principal value of the integral over C with the mean-value of the integrals with the contour displaced
Cauchy_principal_value
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
2021) Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Expression in calculus
is called the mean (or average) value of the derivative of f over the interval [a, b]. This name is justified by the mean value theorem, which states
Difference_quotient
Relation between frequency- and time-domain behavior at large time
In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain
Final_value_theorem
Provides integral formulas for all derivatives of a holomorphic function
1939, p. 84 "Gauss's Mean-Value Theorem". Wolfram Alpha Site. Pompeiu 1905 Hörmander 1966, Theorem 1.2.1 Lebl 2025, p. 130, Theorem 4.1.1 (Cauchy–Pompieu)
Cauchy's_integral_formula
Simplified instance of a general theorem
which is obtained from the mean value theorem by equating the function values at the endpoints. Corollary Fundamental theorem Lemma (mathematics) Toy model
Toy_theorem
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
with values in Rn−r. If v1, ..., vn−r is another such collection of solutions, one can show (using some linear algebra and the mean value theorem) that
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
2.71828...; base of natural logarithms
Mathematics. Dover. pp. 44–48. A standard calculus exercise using the mean value theorem; see for example Apostol (1967) Calculus, § 6.17.41. Sloane, N. J
E_(mathematical_constant)
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Method in statistics
0} . To begin, we use the mean value theorem (i.e.: the first order approximation of a Taylor series using Taylor's theorem): g ( X n ) = g ( θ ) + g
Delta_method
Foundational law of electromagnetism relating electric field and charge distributions
_{0})} Where the last equality follows by the mean value theorem for integrals. Using the squeeze theorem and the continuity of ρ {\displaystyle \rho }
Gauss's_law
Formula in calculus
19–20. ISBN 0-8053-9021-9. Cheney, Ward (2001). "The Chain Rule and Mean Value Theorems". Analysis for Applied Mathematics. New York: Springer. pp. 121–125
Chain_rule
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Integral of sin(x)/x from 0 to infinity
{\displaystyle \sin t} as well as a version of Abel's theorem (a consequence of the final value theorem for the Laplace transform). Therefore, ∫ 0 ∞ sin
Dirichlet_integral
Instantaneous rate of change (mathematics)
input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function
Derivative
Topics referred to by the same term
interpolation formula Lagrange–Bürmann formula Triple product expansion Mean value theorem Euler–Lagrange equation This disambiguation page lists mathematics
Lagrange's_formula
Multivariate derivative (mathematics)
gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle
Gradient
Methods of calculating definite integrals
e. f ∈ C 1 ( [ a , b ] ) . {\displaystyle f\in C^{1}([a,b]).} The mean value theorem for f , {\displaystyle f,} where x ∈ [ a , b ) , {\displaystyle x\in
Numerical_integration
Belgian mathematician (1954–2018)
Together with Ciprian Demeter and Larry Guth, he proved Vinogradov's mean-value theorem in 2015. Bourgain was diagnosed with pancreatic cancer in late 2014
Jean_Bourgain
Indian mathematician and astronomer (1114–1185)
derivative. In his works, there are traces of a special case of mean value theorem. The mean value formula for inverse interpolation of the sine was later formulated
Bhāskara_II
Commutativity of certain mathematical operations
using the mean value theorem for real-valued functions, the same method can be applied for higher-dimensional functions by using the mean value inequality
Interchange of limiting operations
Interchange_of_limiting_operations
Rolle's theorem was given by Michel Rolle in 1691 using methods developed by the Dutch mathematician Johann van Waveren Hudde. The mean value theorem in its
History_of_calculus
queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths
Mean_value_analysis
differentiation theorem (real analysis) Luzin's theorem (real analysis) Malgrange preparation theorem (singularity theory) Mean value theorem (calculus) Monotone
List_of_theorems
Integration over a non-flat region in 3D space
position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it
Surface_integral
Technique in integral evaluation
other one, and they have the same value. Another very general version in measure theory is the following: Theorem—Let X be a locally compact Hausdorff
Integration_by_substitution
Operation in calculus
theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated. Let f be a continuous real-valued function
Integral
Mathematical theorem
critical point somewhere in between. (Think along the lines of the mean-value theorem.) The mountain pass lies along the path that passes at the lowest
Mountain_pass_theorem
Statistical theorem
estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. The Rao–Blackwell theorem states that if δ ( X ) {\displaystyle
Rao–Blackwell_theorem
Cauchy–Schwarz inequality Cauchy space Cauchy's mean value theorem Cauchy's theorem (geometry) Cauchy's theorem (group theory) Cauchy's two-line notation Binet–Cauchy
List of things named after Augustin-Louis Cauchy
List_of_things_named_after_Augustin-Louis_Cauchy
Topics referred to by the same term
Marginal value theorem, a behavioral ecology theorem Mechanical Vapor Transfer, a desalination technology by distillation Mean value theorem, a mathematical
MVT
Russian mathematician (1937–2008)
there entitled "The method of trigonometric sums and intermediate value theorems" in 1966. He later held a position at the Steklov Institute of Mathematics
Anatoly_Karatsuba
&{\text{otherwise}}.\end{array}}\right.} It is derived from the mean value theorem, which states that a secant line, cutting the graph of a differentiable
Stolarsky_mean
Matrix of partial derivatives of a vector-valued function
valued functions of several variables. This generalization includes generalizations of the inverse function theorem and the implicit function theorem
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Mathematical relation consisting of a multi-variable function equal to zero
y is restricted to nonnegative values. Some equations do not admit an explicit solution. The implicit function theorem provides conditions under which
Implicit_function
Branch of mathematics
the harmonic series; both are also credited with formulating the mean speed theorem. Johannes Kepler's work Stereometria Doliorum (1615) formed the basis
Calculus
Hungarian-American mathematician and educator (1887–1985)
Annals of Mathematics Studies 27, 1951 Pólya, G. (1922). "On the mean-value theorem corresponding to a given linear homogeneous differential equation"
George_Pólya
Mathematical theorem, used in calculus
continuous and invertible function. It follows from the intermediate value theorem that f {\displaystyle f} is strictly monotone. Consequently, f {\displaystyle
Integral_of_inverse_functions
Type of average of a collection of numbers
the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or
Arithmetic_mean
Integrals not expressible in closed-form from elementary functions
elementary function. A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis
Nonelementary_integral
Indian mathematician (1943–2023)
Arithmetica 38, 157 in 19 On a theorem of Erdos and Szemeredi, Hardy Ramanujan Journal 3, 41, in 1980 On the Mean Square Value theorem of Hurwitz Zeta function
Mangala_Narlikar
Mathematical function
}\approx 0.56} ) appearing in these bounds are the best possible. The mean value theorem implies the following analog of Gautschi's inequality: If x > c, where
Digamma_function
3D generalization of the Leibniz integral rule
calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds
Reynolds_transport_theorem
Device measuring the speed of a moving vehicle
between the points by the time taken to travel between them. The mean value theorem implies that at some time between the measurements the vehicle's speed
VASCAR
Mathematical techniques used in probability theory and related fields
Clark–Ocone theorem, which allows the process in the martingale representation theorem to be identified explicitly. A simplified version of this theorem is as
Malliavin_calculus
Algorithm for finding zeros of functions
{\begin{aligned}X_{0}&=X\\X_{k+1}&=N(X_{k})\cap X_{k}.\end{aligned}}} The mean value theorem ensures that if there is a root of f in Xk, then it is also in Xk
Newton's_method
Method of mathematical integration
\liminf _{k}\int f_{k}\,d\mu .} Again, the value of any of the integrals may be infinite. Dominated convergence theorem: Suppose {fk}k∈N is a sequence of complex
Lebesgue_integral
approximation theorem Lagrange's formula (disambiguation) Lagrange's identity Lagrange's identity (boundary value problem) Lagrange's mean value theorem Lagrange's
List of things named after Joseph-Louis Lagrange
List_of_things_named_after_Joseph-Louis_Lagrange
Matrix of second derivatives
non-singular points where the Hessian determinant is zero. It follows by Bézout's theorem that a cubic plane curve has at most 9 inflection points, since the Hessian
Hessian_matrix
To find the minimal surface with a given boundary
singular set of dimension at most k − 2 {\displaystyle k-2} in his regularity theorem. S. X. Chang, a student of Almgren, built upon Almgren’s work to show that
Plateau's_problem
Construction in transcendental number theory
{p}{q}}\right)\right|\geq {\frac {1}{q^{d}}},} and also, using the mean value theorem, that there is some constant depending on α, say c(α), such that |
Auxiliary_function
Class of irrational numbers
assume that p q < α {\displaystyle {\tfrac {p}{q}}<\alpha } . By the mean value theorem, there exists x 0 ∈ ( p q , α ) {\displaystyle x_{0}\in \left({\tfrac
Liouville_number
Concept in differential equation mathematics
displacement and external forces, respectively. Using the extended mean value theorem, the Newmark- β {\displaystyle \beta } method states that the first
Newmark-beta_method
according by the mean value theorem for divided differences. The identric mean is a special case of the Stolarsky mean. Mean Logarithmic mean RICHARDS, KENDALL
Identric_mean
Mathematical approximation of a function
function, which become generally more accurate as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such
Taylor_series
Vector operator in vector calculus
would thus have a positive value. While the air is cooled and thus contracting, the divergence of the velocity has a negative value. In physical terms, the
Divergence
Theorem of queueing theory about instantaneous behavior at arrival times
discipline within the mathematical theory of probability, the arrival theorem (also referred to as the random observer property, ROP or job observer
Arrival_theorem
Statistical method for multiple testing
The harmonic mean p-value (HMP) is a statistical technique for addressing the multiple comparisons problem that controls the strong-sense family-wise error
Harmonic_mean_p-value
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
Male
Hebrew
Short form of Hebrew Immanuw'el (English Immanuel), MAN means "God is with us."
Male
English
Anglicized form of Irish Gaelic Cian, KEAN means "ancient, distant."
Male
French
A derivative of Anglo-Norman French Jehan, JEAN means "God is gracious." Compare with feminine Jean.
Girl/Female
American, British, English
Of High Value
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Female
English
Pet form of Welsh Mared, MEGAN means "pearl."Â
Boy/Male
Australian, Finnish
Rule
Boy/Male
Indian
Value, Price
Girl/Female
Arabic
Value; Price
Boy/Male
Hindu, Indian
Value
Boy/Male
Arabic
Value
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English vale (Old French val, from Latin vallis). The surname is now also common in Ireland, where it has been Gaelicized as de Bhál.Galician and Aragonese : topographic name from val ‘valley’, or habitational name from any of the places named with this word.
Girl/Female
Muslim/Islamic
Value Worth
Girl/Female
American, British, English, Italian
Of High Value
Male
English
Anglicized form of Irish Gaelic Seán, SEAN means "God is gracious."
Surname or Lastname
English
English : topographic name from Middle English dene ‘valley’ (Old English denu), or a habitational name from any of several places in various parts of England named Dean, Deane, or Deen from this word. In Scotland this is a habitational name from Den in Aberdeenshire or Dean in Ayrshire.English : occupational name for the servant of a dean or nickname for someone thought to resemble a dean. A dean was an ecclesiastical official who was the head of a chapter of canons in a cathedral. The Middle English word deen is a borrowing of Old French d(e)ien, from Latin decanus (originally a leader of ten men, from decem ‘ten’), and thus is a cognate of Deacon.Irish : variant of Deane.Italian : occupational name cognate with 2, from Venetian dean ‘dean’, a dialect form of degan, from degano (Italian decano).
Male
English
 English occupational surname transferred to forename use, from the Latin word decanus, DEAN means "dean; ecclesiastical supervisor."
Female
English
Scottish form of French Jeanne, JEAN means "God is gracious." Compare with masculine Jean.
Boy/Male
Muslim
Value, Price
Surname or Lastname
Irish
Irish : shortened form of McMeans.English : habitational names from East and West Meon in Hampshire, which take their names from the Meon river. The word is Celtic but of uncertain meaning, possibly ‘swift one’.nickname from Middle English mene ‘inferior in rank’, ‘of low degree’ (from Old English gemǣne), or from Middle English mene ‘moderate in behaviour’ (from Old French mëen, mean).
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
Girl/Female
Indian
Goddess; Study
Boy/Male
Afghan, Arabic, Indian, Muslim
Lamp; Light
Girl/Female
Indian, Punjabi, Sikh
Love Between Each Other
Boy/Male
Hindu
An epithet of Shiva
Surname or Lastname
English, Scottish, German, Dutch, etc.
English, Scottish, German, Dutch, etc. : from the personal name Peter (Greek Petros, from petra ‘rock’, ‘stone’). The name was popular throughout Christian Europe in the Middle Ages, having been bestowed by Christ as a byname on the apostle Simon bar Jonah, the brother of Andrew. The name was chosen by Christ for its symbolic significance (John 1:42, Matt. 16:18); St. Peter is regarded as the founding head of the Christian Church in view of Christ’s saying, ‘Thou art Peter and upon this rock I will build my Church’. In Christian Germany in the early Middle Ages this was the most frequent personal name of non-Germanic origin until the 14th century. This surname has also absorbed many cognates in other languages, for example Czech Petr, Hungarian Péter. It has also been adopted as a surname by Ashkenazic Jews.
Surname or Lastname
English
English : patronymic from Eade.Scottish and Irish : alternate Anglicization of Gaelic Mac Aoidh (see McKay).
Female
English
Variant spelling of English Polly, POLLIE means "obstinacy, rebelliousness" or "their rebellion."Â
Girl/Female
French
From the countly estate.
Girl/Female
Muslim
Leader, Fem of Nasim, Zephyr, Gentle
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
MEAN VALUE-THEOREM
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
superl.
Wanting dignity of mind; low-minded; base; destitute of honor; spiritless; as, a mean motive.
superl.
Of poor quality; as, mean fare.
n.
One who values; an appraiser.
superl.
Penurious; stingy; close-fisted; illiberal; as, mean hospitality.
superl.
Of little value or account; worthy of little or no regard; contemptible; despicable.
n.
Of comparatively small value; common; mean.
imp. & p. p.
of Mean
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
n.
Value.
n.
A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean. A geometrical mean is the square root of the product of the quantities.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
imp. & p. p.
of Value
v. t.
To be worth; to be equal to in value.
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
v. i.
Wanting fullness, richness, sufficiency, or productiveness; deficient in quality or contents; slender; scant; barren; bare; mean; -- used literally and figuratively; as, the lean harvest; a lean purse; a lean discourse; lean wages.
a.
Average; having an intermediate value between two extremes, or between the several successive values of a variable quantity during one cycle of variation; as, mean distance; mean motion; mean solar day.
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.