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Samenvatting VWO Wiskunde d Getal & Ruimte H6
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Samenvatting VWO Wiskunde d Getal & Ruimte H6
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(in iaire differentievergel king van de eerste Oorde recursieveFormule: Un = a .
Un -
, tb
b differentievergel king Un= a Un -1 tb .
liggen de punten
(Una , Un) op de l ny =
axtb
een webgrafiek Un = a. Un -
itb is een diagram dat bestaat uit
aaneengesloten horizontale en verticale l nstukken waarvan de
eindpunten op de l nen g-axtb en g- ✗ liggen de webgrafiek .
begint in het punt 140,0) Het eerste l nstuk is het verticale .
l nstuk met eindpunt op de van
y axtb
=
grafiek
4- = dekpunt .
als Uo = Ú dan is Un een constante r
op één punt richten stabiel evenwicht 4- grenswaarde
convergeren
= . en =
directe Formule Un = A
"
van Un = a
.
Un -
itb is .
a t Û
L constante
b logistischegroei hoort de differentievergel king Pepe + k.pt (I PÉ)
-
.
:
, .
.
G- Grenswaarde
K=
groeivoet groeivoet
stelsel differentievergel kingen : Pt =
1,25 Pt -
i
-
Q 0015 Rt-1 Pt -1
Rt =
Q 97 Rt it 0,00004 Pt
- -
i Rt -1
met Po =
700 en Ro =
200
-
recursieve Formule: Un = a Un it be Um .
.
.
> met b=/0 lineaire
differentievergel king van de tweede Oorde
-
snbstit neer Un =
9
"
-
D 92 ag- -
5- 0 Karakteristieke vergel king
los op .
Oplossingen z n 9 , &
92
A. (g)ÎB (
"
stel nu Un = )
gr
.
directe Formule Un it b. Un -2 met start waarden Uo
-
Un =
a- -
en U,
92
1- >
substitutie gn = → b met D= a + ub
un
ag
- -
"
D >o ?
"
Za .
9, en 92 → Un = A. 9 , + B- 9,
"3-
D= o ?
"
un
=
(AtBn) 9 .
( ☐ 10 =
geen oplossing)
ij
ij
ijijij
ij ij ijijijij
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