Exam (elaborations)
Oefentoets WisB H9 + aw - 5VWO
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Dit is een oefentoets van Wiskunde H9 uit het boek Getal en ruimte deel 3
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Oefenvragen 5VwbOpgave 1
Herleid tot één logaritme.
5
a log( 251 5)
4e
b 3ln 2 2 ln 2 (e3 )
e
1
c 4
log(32) 4log(16) 4 log(8)
Opgave 2
Los algebraïsch en exact op.
a
5
log(x ) 1 5 log( x 4)
1 1
b 2
log 2 ( x ) log( x ) 6
2
c 2 x 3 2 x 6
d 6 ln( x 3) 7 12 ln( x 3)
e e2 x1 3 e2 x 0
f 2 2 x 1 2 x 4 4 x 2 x 1
Opgave 3
a) Welke vermenigvuldiging ten opzichte van de x-as levert bij de grafiek van y ( 21 )
x
dezelfde beeldfiguur op als de translatie (4, 0)?
Licht je antwoord toe.
1
b) Welke translatie levert bij de grafiek van y 2 log( x ) dezelfde beeldfiguur op als de
vermenigvuldiging ten opzichte van de y-as met 8?
Licht je antwoord toe.
Opgave 4
1 1
Gegeven zijn de functies f ( x ) log(2 x ) en g ( x ) 3 log( x 2) .
2 2
Los algebraïsch op f(x) ≤ g(x).
Opgave 5
Differentieer.
a f ( x) 2 x ln 2 ( x 1)
b g ( x ) x 2 1 e5 x
c h( x) 5log( x 4 1)
22 x 1
d j ( x) 1 x2
83
z.o.z.
, Opgave 6
Voor elke waarde van p is gegeven de functie f p ( x) ( p 12 x 2 )e x .
a Bereken exact de extreme waarden van f 4 .
De grafiek van f 2 snijdt de x-as in de punten A(2, 0) en B.
b Stel algebraïsch de formule op van de lijn k die de grafiek van f 2 raakt in B.
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