Rekenregels Kwadratische vergelijking Limieten
y = ax2 + bx + c = 0 Horizontale asymptoot
(a · b) · c = a · (b · c) √ lim f (x) = a
x→±∞
a · (b + c) = a·b+a·c −b ± b2 − 4ac 2
x1,2 = D = b − 4ac Verticale asymptoot
(a + b) · (c + d) = ac + ad + bc + bd 2a
b b
Machten D>0 2 oplossingen lim f (x) = = = ±∞
x→a (x − a) 0
am · an = am+n
D=0 1 oplossing
am Perforatie
an
= am−n D<0 geen oplossing 0
m n
(a ) = am·n lim f (x) = = NA
(x − x1 ) · (x − x2 ) x→a 0
a0 = 1 → Nulpunt wegdelen
a−n = 1
an
√ 1
Schuine asymptoot
a = a2 Goniometrie
(ab)c
= ac · bc√ → Staartdeling
√ 1 √ Eenheidscirkel (r = 1cm)
a · b = (ab) 2 = √
a· b π
pa
= √
a 2π 2 π Differentiëren
b b 3π 3 √ 3 π θ
√ 4
1
2√
3 4
3 1
f (x) = xn → f ′ (x) = nxn−1
√a = a3 1
2
2
5π π
3
a2 =
2
a3 6
1
2 6 c · f (x) → c · f ′ (x)
f (x) · g(x) → f ′ (x) · g(x) + f (x) · g ′ (x)
Breuken π cos(x)→ x-as f (g(x)) → f ′ (g(x)) · (g ′ (x))
ab
a × (b : c) = sin(x)→ y-as f (x) f ′ (x)g(x)−f (x)g ′ (x)
c
a 1 a → (g(x))2
(a : b) /c = b
· c
= bc
7π 11π g(x)
d
a / (b : c) = a
· c
= ac 6 6
dx
(sin x) → cos x
1 b b d
5π 7π
dx
(cos x) → − sin x
4 4π 5π 4
Logaritmes 3 3π 3
d d
y =g log(x) ↔ gy = x 2
d x dx
(ax)
= dx (ex ln a )
e
log(x) ↔ ln(x) (e ) = ex x
= a · ln(a)
a + b sin(c(x − d)) dx
g log(x)
log(x) = log(g) a = evenwichtstand
y d g d ln(
g
log(ab) = g
log(a) + g log(b) y = ln x → e = x ( log x) =
b = amplitude dy
dx dx ln(
g
log( ab ) = g
log(a) − g log(b) 2π *ey · dx =1 d
= ln(g) · dx (ln(x))
c = periode
g
log(an ) = n ·g log(a) d = verschuiving d 1 1
(ln x) = =
dx x x · ln(g)
Staartdeling α
Delen van een veelterm door (x-a): Integreren
x2 − 1 R
f (x) = R c ndx = cx + c
x−2 1
· xn+1 +Rc (n
R x dx = Rn+1
x2 −1 x − 2 R (f (x) + g(x))
′
dx = R f (x) dx + g(x)
2
−(x −2x ) x +2 −α R f (g(x))g (x) dx = f (u) du (u = g(
y = ax2 + bx + c = 0 Horizontale asymptoot
(a · b) · c = a · (b · c) √ lim f (x) = a
x→±∞
a · (b + c) = a·b+a·c −b ± b2 − 4ac 2
x1,2 = D = b − 4ac Verticale asymptoot
(a + b) · (c + d) = ac + ad + bc + bd 2a
b b
Machten D>0 2 oplossingen lim f (x) = = = ±∞
x→a (x − a) 0
am · an = am+n
D=0 1 oplossing
am Perforatie
an
= am−n D<0 geen oplossing 0
m n
(a ) = am·n lim f (x) = = NA
(x − x1 ) · (x − x2 ) x→a 0
a0 = 1 → Nulpunt wegdelen
a−n = 1
an
√ 1
Schuine asymptoot
a = a2 Goniometrie
(ab)c
= ac · bc√ → Staartdeling
√ 1 √ Eenheidscirkel (r = 1cm)
a · b = (ab) 2 = √
a· b π
pa
= √
a 2π 2 π Differentiëren
b b 3π 3 √ 3 π θ
√ 4
1
2√
3 4
3 1
f (x) = xn → f ′ (x) = nxn−1
√a = a3 1
2
2
5π π
3
a2 =
2
a3 6
1
2 6 c · f (x) → c · f ′ (x)
f (x) · g(x) → f ′ (x) · g(x) + f (x) · g ′ (x)
Breuken π cos(x)→ x-as f (g(x)) → f ′ (g(x)) · (g ′ (x))
ab
a × (b : c) = sin(x)→ y-as f (x) f ′ (x)g(x)−f (x)g ′ (x)
c
a 1 a → (g(x))2
(a : b) /c = b
· c
= bc
7π 11π g(x)
d
a / (b : c) = a
· c
= ac 6 6
dx
(sin x) → cos x
1 b b d
5π 7π
dx
(cos x) → − sin x
4 4π 5π 4
Logaritmes 3 3π 3
d d
y =g log(x) ↔ gy = x 2
d x dx
(ax)
= dx (ex ln a )
e
log(x) ↔ ln(x) (e ) = ex x
= a · ln(a)
a + b sin(c(x − d)) dx
g log(x)
log(x) = log(g) a = evenwichtstand
y d g d ln(
g
log(ab) = g
log(a) + g log(b) y = ln x → e = x ( log x) =
b = amplitude dy
dx dx ln(
g
log( ab ) = g
log(a) − g log(b) 2π *ey · dx =1 d
= ln(g) · dx (ln(x))
c = periode
g
log(an ) = n ·g log(a) d = verschuiving d 1 1
(ln x) = =
dx x x · ln(g)
Staartdeling α
Delen van een veelterm door (x-a): Integreren
x2 − 1 R
f (x) = R c ndx = cx + c
x−2 1
· xn+1 +Rc (n
R x dx = Rn+1
x2 −1 x − 2 R (f (x) + g(x))
′
dx = R f (x) dx + g(x)
2
−(x −2x ) x +2 −α R f (g(x))g (x) dx = f (u) du (u = g(
