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Formally, the derivative of the function f at a is the limit

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## Some Related Sentences

Formally and derivative

__Formally__

**,**they are partial derivatives

**of**

**the**option price with respect to

**the**independent variables ( technically

**,**one Greek

**,**gamma

**,**

**is**

**a**partial

__derivative__

**of**another Greek

**,**called delta ).

Formally and function

__Formally__

**,**there

**is**

**a**clear distinction: " DFT " refers to

**a**mathematical transformation or

__function__

**,**regardless

**of**how it

**is**computed

**,**whereas " FFT " refers to

**a**specific family

**of**algorithms for computing DFTs.

__Formally__

**,**if M

**is**

**a**set

**,**

**the**identity

__function__

**f**on M

**is**defined to be that

__function__with domain and codomain M which satisfies

__Formally__

**,**

**the**discrete cosine transform

**is**

**a**linear

**,**invertible

__function__( where denotes

**the**set

**of**real numbers ), or equivalently an invertible N × N square matrix.

__Formally__

**,**we are given

**a**set

**of**hypotheses and

**a**set

**of**manifestations ; they are related by

**the**domain knowledge

**,**represented by

**a**

__function__that takes as an argument

**a**set

**of**hypotheses and gives as

**a**result

**the**corresponding set

**of**manifestations.

__Formally__

**,**

**a**

__function__ƒ

**is**real analytic on an open set D in

**the**real line if for any x < sub > 0 </ sub > in D one can write

__Formally__

**,**an elliptic

__function__

**is**

**a**

__function__meromorphic on for which there exist two non-zero complex numbers and with ( in other words

**,**not parallel ), such that and for all.

__Formally__

**,**if

**is**an open subset

**of**

**the**complex plane

**,**

**a**point

**of**

**,**and

**is**

**a**holomorphic

__function__

**,**then

**is**called

**a**removable singularity for if there exists

**a**holomorphic

__function__which coincides with on.

__Formally__

**,**

**the**problem

**of**supervised pattern recognition can be stated as follows: Given an unknown

__function__(

**the**ground truth ) that maps input instances to output labels

**,**along with training data assumed to represent accurate examples

**of**

**the**mapping

**,**produce

**a**

__function__that approximates as closely as possible

**the**correct mapping.

__Formally__

**,**

**a**statistic s

**is**

**a**measurable

__function__

**of**X ; thus

**,**

**a**statistic s

**is**evaluated on

**a**random variable X

**,**taking

**the**value s ( X ), which

**is**itself

**a**random variable.

__Formally__

**,**

**the**discrete sine transform

**is**

**a**linear

**,**invertible

__function__F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > ( where R denotes

**the**set

**of**real numbers ), or equivalently an N × N square matrix.

__Formally__

**,**

**the**discrete Hartley transform

**is**

**a**linear

**,**invertible

__function__H: R < sup > n </ sup > < tt >-></ tt > R < sup > n </ sup > ( where R denotes

**the**set

**of**real numbers ).

__Formally__

**,**

**a**cardinal κ

**is**defined to be weakly compact if it

**is**uncountable and for every

__function__

**f**: < sup > 2 </ sup > →

__Formally__

**,**an analytic

__function__ƒ ( z )

**of**

**the**real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub >

**is**transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z ) are algebraically independent

**,**i. e., if ƒ

**is**transcendental over

**the**field C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).

__Formally__

**,**this means that

**,**for some

__function__

**f**

**,**

**the**image

**f**( D )

**of**

**a**directed set D ( i. e.

**the**set

**of**

**the**images

**of**each element

**of**D )

**is**again directed and has as

**a**least upper bound

**the**image

**of**

**the**least upper bound

**of**D. One could also say that

**f**preserves directed suprema.

__Formally__

**,**let be

**a**stochastic process and let represent

**the**cumulative distribution

__function__

**of**

**the**joint distribution

**of**

**at**times.

__Formally__

**,**an ultrametric space

**is**

**a**set

**of**points with an associated distance

__function__( also called

**a**metric )

Formally and f

__Formally__

**,**an absolute coequalizer

**of**

**a**pair in

**a**category C

**is**

**a**coequalizer as defined above but with

**the**added property that given any functor F ( Q ) together with F ( q )

**is**

**the**coequalizer

**of**F (

__f__) and F ( g ) in

**the**category D. Split coequalizers are examples

**of**absolute coequalizers.

__Formally__

**,**given two partially ordered sets ( S

**,**≤) and ( T

**,**≤),

**a**

**function**

__f__: S → T

**is**an order-embedding if

__f__

**is**both order-preserving and order-reflecting

**,**i. e. for all x and y in S

**,**one has

__Formally__

**,**

**the**bounded Borel functional calculus

**of**

**a**self adjoint operator T on Hilbert space H

**is**

**a**mapping defined on

**the**space

**of**bounded complex-valued Borel functions

__f__on

**the**real line

**,**

__Formally__

**,**

__f__< sub > X

**,**Y </ sub >( x

**,**y )

**is**

**the**probability density

**function**

**of**( X

**,**Y ) with respect to

**the**product measure on

**the**respective supports

**of**X and Y.

__Formally__

**,**if

__f__

**is**

**a**harmonic

**function**

**,**then

__f__cannot exhibit

**a**true local maximum within

**the**domain

**of**definition

**of**

__f__. In other words

**,**either

__f__

**is**

**a**constant

**function**

**,**or

**,**for any point inside

**the**domain

**of**

__f__

**,**there exist other points arbitrarily close to

**at**which

__f__takes larger values.

__Formally__

**,**if we denote

**the**set

**of**stable functions by S ( D ) and

**the**stability radius by r (

__f__

**,**D ), then:

Formally and at

More rigorously

**,****the**divergence**of****a**vector field F__at__**a**point p**is**defined as**the****limit****of****the**net flow**of**F across**the**smooth boundary**of****a**three dimensional region V divided by**the**volume**of**V as V shrinks to p.__Formally__**,**
In late 1900s

**the**day that**of****the**City was founded**is**Jakin School**is****a**Private School**is**__Formally__Part**of**Jakin School Board was Grades One through Twelve there**is**no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary**,**Junior High**,**and High School ( which later Became Early County High**,**Middle**,**and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary__at__Blakely. In addition to small farm agriculture**,**Jakin's early economic growth resulted from turpentine.__Formally__known as

**the**Kingfisher Pier

**,**

**the**Pier

__at__Garden City

**is**one

**of**

**the**most renowned attractions in Garden City

**,**SC.

__Formally__

**,**it

**is**

**a**coalition

**of**U. S. and European CEOs

**,**largely from transnational corporations

**,**launched

__at__

**the**urging

**of**former United States Secretary

**of**Commerce Ron Brown in Seville ( Spain ) in late 1995

__at__

**a**conference attended by CEOs from more than 100 U. S. and EU companies and by top government representatives led by

**the**Commissioners for Trade and Industry and by

**the**U. S. Secretary

**of**Commerce.

__Formally__

**,**

**the**outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data

**,**where each outcome

**is**determined by an unobserved probability p < sub > i </ sub > that

**is**specific to

**the**outcome

__at__hand

**,**but related to

**the**explanatory variables.

__Formally__

**,**an nth order approximation

**is**one where

**the**order

**of**magnitude

**of**

**the**error

**is**

__at__most

**,**or in terms

**of**big O notation

**,**

**the**error

**is**

By 1912

**,****the**Social Democrats**,**with an explicitly anti-antisemitic program**,**were**the**largest party in**the**German Reichstag**,**and**the**Progressives ran very strongly as well ...__Formally__**,**__at__least**,****the**Jews had been fully emancipated with**the**establishment**of****the**German Empire**,**although they were kept out**of**certain influential occupations**,**enjoyed extraordinary prosperity ... Germans intermarried with Jews: in**the**1930s some 50**,**000 Jews were living in mixed German-Jewish marriages**,**so__at__least 50**,**000 Germans**,**and presumably parts**of**their families**,**had familial contact with**the**Jews.__Formally__

**the**Guild

**of**Fools and Joculators and College

**of**Clowns ( described in Wyrd Sisters and appears in Men

__at__Arms and Making Money )

__Formally__

**,**if R

**is**

**a**Noetherian ring and I

**is**

**a**principal

**,**proper ideal

**of**R

**,**then I has height

__at__most one.

__Formally__

**,**Mbenga – Mbuti Pygmy music consists

**of**

__at__most only four parts

**,**and can be described as an

**,**" ostinato with variations ," or similar to

**a**passacaglia

**,**in that it

**is**cyclical.

__Formally__

**,**

**a**vertex cover

**of**

**a**graph G

**is**

**a**set C

**of**vertices such that each edge

**of**G

**is**incident to

__at__least one vertex in C. The set C

**is**said to cover

**the**edges

**of**G. The following figure shows examples

**of**vertex covers in two graphs ( and

**the**set C

**is**marked with red ).

__Formally__nicknamed

**the**" Pacemaker " by

**a**staffer

__at__Peterbilt after an in-house name contest in 1969 (

**the**winner got

**a**color TV ).

Many interior sets were built

__at__**the**Castle Brae Business Centre (__Formally__**the**Castlebrae High School ) in Edinburgh.
Several significant events in 2001 persuaded BNFL to upgrade

**the**fuel routes**of**both Calder Hall and Chapelcross to near modern standards__at__**a**cost**of**tens**of**millions**of**pounds to guarantee that**a**License Instrument would be granted by**the**NII to permission final defuelling:**the**engineering work**is**being carried out by BNS Nuclear Services (__Formally__Alstec ).__Formally__

**,**an " Order in Council "

**is**an order by

**the**King or Queen

__at__

**a**meeting

**of**

**the**Privy Council

**,**roughly equivalent to an Executive Order in

**the**United States

**,**by which

**the**British government decrees policies.

__Formally__known as

**the**' Little Monsters Den

**of**Mischief ', this area

**is**mainly aimed

__at__children

**,**and includes

**the**attractions Little Monster's Wacky Races and Mischief Mansion.

__Formally__introduced in 1991

**,**Gut Recordings was founded by Guy Holmes

**,**who had been Head

**of**Promotions

__at__Island Records.

__Formally__accepted as

**a**candidate for

**the**Franciscan Order

__at__Christ House in Lafayette

**,**New Jersey

**,**in 1970

**,**

**the**following year he entered

**the**novitiate

**of**

**the**Order

__at__St. Francis Friary in Brookline

**,**Massachusetts

**,**where he professed his first vows in 1972.

__Formally__based

__at__

**the**RHQ 95 Horseferry road until 2005 and now

__at__

**the**former RMP barracks on Rochester row.

0.134 seconds.