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Die gradiënt van 'n reguitlyngrafiek word bereken met:

y 2 - y 1 x 2 - x 1

vir 2 punte ( x 1 ; y 1 ) en ( x 2 ; y 2 ) op die grafiek.

Ons kan nou die gemiddelde gradiënt tussen 2 punte ( x 1 ; y 1 ) en ( x 2 ; y 2 ) bepaal, selfs al word hulle gedefinieer deur 'n funksie wat nie 'n reguitlyn is nie, met:

y 2 - y 1 x 2 - x 1

Dit is dieselfde as [link] .


Ondersoek: gemiddelde gradiënt - reguitlynfunksie

Voltooi die tabel deur die gemiddelde gradiënt oor die aangeduide intervalle te bereken vir die funksie f ( x ) = 2 x - 2 . Let daarop dat ( x 1 ; y 1 ) die koördinate is van die eerste punt en dat ( x 2 ; y 2 ) die koördinate is van die tweede punt. So, vir AB is ( x 1 ; y 1 ) die koördinate van punt A en ( x 2 ; y 2 ) is die koördinate van punt B.

x 1 x 2 y 1 y 2 y 2 - y 1 x 2 - x 1

Wat let jy op van die gradiënte oor elke interval?

Die gemiddelde gradiënt van 'n reguitlynfunksie is dieselfde oor enige twee intervalle in die funksie.

Paraboliese funksie

Ondersoek : gemiddelde gradiënt - paraboliese funksie

Vul die tabel in deur die gemiddelde gradiënt oor die aangeduide intervalle te bereken vir die funksie f ( x ) = 2 x - 2 :

x 1 x 2 y 1 y 2 y 2 - y 1 x 2 - x 1

Wat let jy op van die gemiddelde gradiënt oor elke interval? Wat kan jy sê oor die gemiddelde gradiënte tussen A en D in vergelyking met die gemiddelde gradiënte tussen D en G?

Die gemiddelde gradiënt van 'n paraboliese funksie hang af van die interval en is die gradiënt van 'n reguitlyn wat deur die betrokke punte op daardie interval loop.

Byvoorbeeld, in [link] is die verskeie punte verbind deur reguitlyne. Die gemiddelde gradiënte tussen die betrokke punte is dan die gradiënte van die reguitlyne wat deur daardie punte loop.

Die gemiddelde gradiënt tussen twee punte op 'n kurwe is die gradiënt van die reguitlyn wat deur die punte loop.

Metode: gemiddelde gradiënt

Gegee, die vergelyking van 'n kromme en twee punte ( x 1 ; x 2 ):

  1. Skryf die vergelyking van die kromme in die vorm y = ... .
  2. Bereken y 1 deur x 1 in die vergelyking vir die kromme in te stel.
  3. Bereken y 2 deur x 2 in die vergelyking vir die kromme in te stel.
  4. Bereken die gemiddelde gradiënt deur gebruik te maak van:
    y 2 - y 1 x 2 - x 1

Vind die gemiddelde gradiënt van die kromme y = 5 x 2 - 4 tussen die punte x = - 3 en x = 3 .

  1. Merk die punte as volg:

    x 1 = - 3
    x 2 = 3

    om dit makliker te maak om die gradiënt te bereken.

  2. Ons gebruik die vergelyking van die kromme om die y -waarde van die kromme by x 1 en x 2 te vind.

    y 1 = 5 x 1 2 - 4 = 5 ( - 3 ) 2 - 4 = 5 ( 9 ) - 4 = 41
    y 2 = 5 x 2 2 - 4 = 5 ( 3 ) 2 - 4 = 5 ( 9 ) - 4 = 41
  3. y 2 - y 1 x 2 - x 1 = 41 - 41 3 - ( - 3 ) = 0 3 + 3 = 0 6 = 0
  4. Die gemiddelde gradiënt tussen x = - 3 en x = 3 op die kromme y = 5 x 2 - 4 is 0.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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s. Reply
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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