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Formuleblad Wiskunde 1

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Course
Wiskunde 1

Institution
Erasmus Universiteit Rotterdam (EUR)

Formuleblad voor Wiskunde 1, studie Economie en Bedrijfseconomie, 1e jaar. Formuleblad bestaat uit twee pagina's. Deze pagina's staan vol met formules die bruikbaar zijn voor het tentamen, o.a. logartimen, limieten, afgeleides, lagrange en nog meer.

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Uploaded on November 9, 2011
Number of pages 2
Written in 2011/2012
Type Other
Person Dr. d.k. leegwater

wiskunde
formules
formuleblad
tentamenblad

Institution
Erasmus Universiteit Rotterdam (EUR)
Education
Economie en Bedrijfseconomie
Course
Wiskunde 1

K_E_V_I_N

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ABC formule : ax2+bx+c 
Drie nulpunten zoeken? Je weet één=a. Dus functie delen door [x-(a)]. (Staartdeling)

ab∙ac = a(b+c)
(ab)c=a(b∙c)
ab∙cb=acb
(ab)/(cb)=(a/c)b f(x)  c*f(x) : c>0 : verticaal uitgerekt
c<0 : verticaal uitgerekt + gespiegeld rond x-as
ax=b  x=ln(b)/ln(a)
f(x)  f(-x) : grafiek gespiegeld rond y-as
y=loga(x)=alog(x)  ay=x
ln(ab)=ln(a) + ln(b)
ln(a/b)= ln(a)-ln(b)
log(p)/log(q)=ln(p)/ln(q)
ln(x)-ln(y)+ln(z)=ln((x∙z)/y)
ln(ab)=b∙ln(a) y = log a x 
e
y1 = (1 / ln a) * (1/x)
log(x) = loge(x) = ln(x) =elog(x)
eln(x)= x
10log (x) = x
ex=y  x=ln(y)
x (vet) = x1, x2, … xn

F f’ f“
√(x) 1/(2√(x)) -1/(4x√(x))
ax ax∙ln(a) (ax∙(ln(a))2)
ex ex ex
a
log(x) 1/(ln(a) ∙x)
ln(x) 1/x -1/x2
xx xx(ln(x)+1)

Convex als f”(x) ≥0
Concaaf als f”(x) ≤ 0

Continuïteit :
a/b bij b≠0
√(c) bij c ≥ 0
ln(d) bij d>0
El y f(x) = y / f(x) * f1(x)
Elasticiteit voor y=f(x)  (x\y) ∙y’ = (x/y) ∙ (dy)/(dx) =
EL x z = d ln z / d ln x El y z = d ln z / d ln y
Inverse:
f(x)=ax  ax = ag(x) g(x) naar voren halen. (Dus eigenlijk y en x omdraaien en y naar links)
g’(x) = 1/(f’(x))
Domein van inverse = bereik basisfunctie Voor stationaire punten bij meerdere variabelen: (voor de
Bereik van inverse = domein basisfunctie tweede afgeleide evt. waarde variabele uit eerste
afgeleide invullen)
Absolute waarde:
|10|= 10 en -10

Maximaliseer onder voorwaarde dat [restrictie]:
(truc Edelenbosch, wel stap 1 & 2 Lagrange
toevoegen)
f(x,y) = Axayb o.v.d. g(x,y) = px+qy=m
x*= (a)/(a+b)*(m/p)
y*=(b)/(a+b)*(m/q)

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