math cheat sheet
Post on 12-Jan-2016
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Quadratic Formula
a x2+bx+c=0
x=−b±√b2−4ac2a
Factoring Polynomials
x2− y2=( x+ y ) ( x− y )
x3+ y3=( x+ y ) (x2−xy+ y2 )
x3− y3= (x− y ) (x2+xy+ y2 )
Natural logs and exponents
f ( x )=ln ( x )
x=e f (x)
f ( x )=ex
x=ln ( f ( x ))
Cealn (b )=Cba
Cea+ln (b )=Cbea
Cea−ln (b)=C ea
b
Ce ln (b)−a=Cbe−a
ln (a∗b )=ln (a )+ln (b )
ln (a /b )=ln (a )−ln (b )
Geometry
Triangle :
A=12bh=1
2ab sin θ
:̊
A=π r2
C=2πr
Product Rule
h ( x )=f (x ) g ( x )
h' ( x )=g ( x ) f ' ( x )+f ( x )g ' ( x )
Quotient Rule
h ( x )= f ( x )g (x )
h' ( x )=g ( x ) f ' ( x )−f ( x )g ' ( x )
[ g ( x ) ]2
Lagrange Multipliers
Given f ( x , y ) s . t . g (x , y )=0 ,
L ( x , y , λ )=f ( x , y )+λg ( x , y )
Set∂L∂ x
=0 , ∂ L∂ y
=0 , ∂ L∂ λ
=0
OR
Given f ( x , y ) s . t . g (x , y )=k ,
f x ( x , y )=λ gx (x , y )
f y ( x , y )=λ g y ( x , y )
g ( x , y )=k
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