Exam (elaborations)
Tentamen Calculus december 2012
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December tentamen van het vak Calculus
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Faculteit der Exacte Wetenschappen Tentamen Calculus I8.45-10.45
Vrije Universiteit 24-12-2010
• Gebruik van rekenmachine, formuleblad of aantekeningen is niet toegestaan.
• Dit tentamen bestaat uit 5 opgaven met in totaal 9 onderdelen. Ieder onderdeel is
4 punten waard. Er zijn dus in totaal 36 punten te behalen, het eindcijfer wordt
gegeven door (aantal punten+4)/4.
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• Na de correctie liggen de tentamens ter inzage op het onderwijsbureau.
1. Bereken de vergelijking van de raaklijn in het punt (3, 1) aan de kromme
3x
K : x2 y − = 0.
y
√ √
2. Bereken lim x2 − 6x − x2 − 8x.
x→−∞
3. Bepaal alle x ∈ R waarvoor geldt dat
3x + 2
≤ 1.
x2 − 16
4. Bereken de volgende integralen:
Z
a) 4x arctan x dx,
Z
1
b) 2
dx,
x − 3x
√
cos 2x − 1
Z
c) √ dx.
2x − 1
5. Bepaal de algemene oplossing van volgende differentiaalvergelijkingen:
a) y 00 − 4y 0 + 20y = 0,
dy y
b) − 4 = 0,
dx x
dy
c) − xy = x.
dx
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