Eksamenssett.no
Ressurser
Skolenytt
Hoderegning
MET1
Formelark
Matematikk for økonomer
eksamenssett.no
Derivasjon
•
(
x
n
)
′
=
n
x
n
−
1
(x^n)' = nx^{n-1}
(
x
n
)
′
=
n
x
n
−
1
•
(
e
k
x
)
′
=
k
e
k
x
(e^{kx})' = ke^{kx}
(
e
k
x
)
′
=
k
e
k
x
•
(
ln
x
)
′
=
1
x
\displaystyle (\ln x)' = \frac{1}{x}
(
ln
x
)
′
=
x
1
•
(
f
g
)
′
=
f
′
g
+
f
g
′
(fg)' = f'g + fg'
(
f
g
)
′
=
f
′
g
+
f
g
′
•
(
f
g
)
′
=
f
′
g
−
f
g
′
g
2
\displaystyle \left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}
(
g
f
)
′
=
g
2
f
′
g
−
f
g
′
•
(
f
(
g
(
x
)
)
)
′
=
f
′
(
g
(
x
)
)
⋅
g
′
(
x
)
(f(g(x)))' = f'(g(x)) \cdot g'(x)
(
f
(
g
(
x
))
)
′
=
f
′
(
g
(
x
))
⋅
g
′
(
x
)
Integrasjon
•
∫
x
n
d
x
=
x
n
+
1
n
+
1
+
C
\displaystyle \int x^n\,dx = \frac{x^{n+1}}{n+1} + C
∫
x
n
d
x
=
n
+
1
x
n
+
1
+
C
•
∫
1
x
d
x
=
ln
∣
x
∣
+
C
\displaystyle \int \frac{1}{x}\,dx = \ln|x| + C
∫
x
1
d
x
=
ln
∣
x
∣
+
C
•
∫
e
k
x
d
x
=
1
k
e
k
x
+
C
\displaystyle \int e^{kx}\,dx = \frac{1}{k}e^{kx} + C
∫
e
k
x
d
x
=
k
1
e
k
x
+
C
•
∫
a
b
f
(
x
)
d
x
=
F
(
b
)
−
F
(
a
)
\displaystyle \int_a^b f(x)\,dx = F(b) - F(a)
∫
a
b
f
(
x
)
d
x
=
F
(
b
)
−
F
(
a
)
Lineær algebra
•
det
(
A
)
=
a
d
−
b
c
\det(A) = ad - bc
det
(
A
)
=
a
d
−
b
c
•
A
−
1
=
1
det
(
A
)
(
d
−
b
−
c
a
)
\displaystyle A^{-1} = \frac{1}{\det(A)}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}
A
−
1
=
det
(
A
)
1
(
d
−
c
−
b
a
)
•
x
=
A
−
1
b
\mathbf{x} = A^{-1}\mathbf{b}
x
=
A
−
1
b
•
x
i
=
det
(
A
i
)
det
(
A
)
\displaystyle x_i = \frac{\det(A_i)}{\det(A)}
x
i
=
det
(
A
)
det
(
A
i
)
(Cramers regel)
Finansmatematikk
•
F
V
=
P
V
(
1
+
r
)
t
FV = PV(1+r)^t
F
V
=
P
V
(
1
+
r
)
t
•
P
V
=
F
V
(
1
+
r
)
t
\displaystyle PV = \frac{FV}{(1+r)^t}
P
V
=
(
1
+
r
)
t
F
V
•
P
V
annuitet
=
a
⋅
1
−
(
1
+
r
)
−
n
r
\displaystyle PV_{\text{annuitet}} = a \cdot \frac{1-(1+r)^{-n}}{r}
P
V
annuitet
=
a
⋅
r
1
−
(
1
+
r
)
−
n
•
N
P
V
=
−
I
0
+
∑
C
F
t
(
1
+
r
)
t
\displaystyle NPV = -I_0 + \sum \frac{CF_t}{(1+r)^t}
NP
V
=
−
I
0
+
∑
(
1
+
r
)
t
C
F
t
•
P
V
perpetuity
=
C
F
r
\displaystyle PV_{\text{perpetuity}} = \frac{CF}{r}
P
V
perpetuity
=
r
CF
Differensiallikninger
•
y
′
+
a
y
=
b
⇒
y
(
t
)
=
C
e
−
a
t
+
b
a
\displaystyle y' + ay = b \Rightarrow y(t) = Ce^{-at} + \frac{b}{a}
y
′
+
a
y
=
b
⇒
y
(
t
)
=
C
e
−
a
t
+
a
b
•
y
′
=
k
y
⇒
y
(
t
)
=
y
0
e
k
t
y' = ky \Rightarrow y(t) = y_0 e^{kt}
y
′
=
k
y
⇒
y
(
t
)
=
y
0
e
k
t
•
Likevekt
y
∗
=
b
a
\displaystyle y^* = \frac{b}{a}
y
∗
=
a
b
, stabil når
a
>
0
a > 0
a
>
0
Rekker
•
S
n
=
a
⋅
1
−
r
n
1
−
r
\displaystyle S_n = a \cdot \frac{1 - r^n}{1 - r}
S
n
=
a
⋅
1
−
r
1
−
r
n
•
S
=
a
1
−
r
\displaystyle S = \frac{a}{1 - r}
S
=
1
−
r
a
(uendelig,
∣
r
∣
<
1
|r| < 1
∣
r
∣
<
1
)
•
P
V
=
C
F
r
−
g
\displaystyle PV = \frac{CF}{r - g}
P
V
=
r
−
g
CF
(Gordon)