Samenvatting Wiskunde I(A) door Prof. dr. J. Van der Jeugt
H1: Inleidende begrippen
H2: Functies: algemene begrippen en voorbeelden
H3: Limieten en continuïteit
H4: Afgeleiden en differentiaalrekening
()
% De getallen x
stelling van
plantageras
⇒ TE =/ ④ →
Bewijs uit het
ongerijmde
, Rationale getallen
Irrationale getallen
} ⇒ Reële getallen IR
Vvd 52 =
1,144 . . . 1T =
3 14159 . . .
,
→ Teken van X E IR
zien × = t 1 als × > 0
riem × = -
en als × en 0
signs × =
0 als × = 0
Absolute waarde
→
van ×
1X 1 = X als × zo → 1×1 = x. zien ×
1×1 = -
X als X E 0
Intervallen in R
-
*
Eindige intervallen [ a. er] : [ a.
er [ i Ja .
er [ .
. . .
*
Oneindige intervallen [ •
,
te [ ; J - *
,
a ]
f)-
Begrenzing
is de V
Er bovengrens t
→
van ⇐ x ← u : x ← er
Er is de V 78
benedengrens ⇐ t
→
van x E V
:
x
Stellig : Als een
verzameling V ER naar leven begrensd is ,
kleinste
dan heeft de
verzameling van de bovengrenzen een
element .
kleinste
Supreme =
bovengrens
Inferieur grootste ondergrens
, '
N Ja er [ V Er v
eng
:
we *
sap
= = =
a
,
{ In }
*
* V
v = C-
en :
sap
= 2
inz v = 1
( v =
{ 2. 7,7 .
. . . 3
'
2- ⇒ ~
ondergrens
M¥
d
en
= t
is kleinste
x e
ondergrens
( is
1,001 ) geen ondergrens
* v =
{ 1
,
f. 7,7 .
. . .
} soep V = 1 inf v = 0
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