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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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Document information

  • November 9, 2011
  • 2
  • 2011/2012
  • Other
  • Dr. d.k. leegwater

Subjects

  • wiskunde
  • formules
  • formuleblad
  • tentamenblad

Written for

  • Erasmus Universiteit Rotterdam (EUR)
  • Economie en Bedrijfseconomie
  • Wiskunde 1
All documents for this subject (4)

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Content preview

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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