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COLEGIO HEBREO TARBUT 2011-2012 FORMULARIO CÁLCULO DIFERENCIAL E INTEGRAL ÁREA III LÍMITES

f ( x) − l < ε
θ −> 0

lim

senθ tan θ

θ

=1 =1

θ −> 0

lim

θ

DERIVADAS

( c )′ =0
( x )′ = 1

cu ′  c ′   =− 2 u u u′ ′ u = 2 u ( u )′ ( ln u )′ = u eu ′ = e u ⋅ u ′

( )
( )

( cx )′ = c
 x ′ 1   = c c 1  1 ′   =− 2 x x 1 ′ x = 2 x 1 ( ln x )′ = x ex ′= ex

( senu )′ = cos u ⋅ u ′

( cos u )′ = − senu ⋅ u′
( tan u )′ = sec2 u ⋅ u′

( cot u )′ = − csc 2 u ⋅ u′
( sec u )′ = sec u tan u ⋅ u ′

( )
( )

( csc u )′ = − csc u cot u ⋅ u′INTEGRALES

∫ dx = x + c ∫ cdu = c ∫ du
x n +1 +c n +1 x x ∫ e dx = e + c
n ∫ x dx =

( senx )′ = cos x

( cos x )′ = − senx

( u + v − w)′ = u´+v´− w´ ( cu )′ = c ( u )´ ( uv )´= uv´+vu´

(u )′ = nu ( u )´
n n −1

∫ sen ( x ) dx = − cos ( x ) + c ∫ cos ( x ) dx = sen ( x ) + c dx ∫ x = ln x + c ∫ ( du + dv − dw ) = ∫ du + ∫ dv − ∫ dw
u n+1 ∫ u du = n + 1 + c du ∫ u = ln u + c
n u ′ v ( u )´−u ( v )´   = v2 v  u ′ u ′   = c c

COLEGIO HEBREO TARBUT 2011-2012 FORMULARIO CÁLCULO DIFERENCIAL E INTEGRAL ÁREA III

∫ ax ± b = a ln ax ± b + c ∫ e du = e + c ∫senudu = − cos u + c ∫ cos udu = senu + c ∫ tan udu = ln sec u + c ∫ cot udu = − ln csc u + c ∫ sec udu = ln ( sec u + tan u ) + c ∫ csc udu = ln ( csc u − cot u ) + c ∫ sec udu = tan u + c ∫ csc udu = −cot u + c ∫ csc u cot udu = − csc u + c ∫ sec u tan udu = sec u + c
u u 2

dx

1

INTEGRAL DEFINIDA

∫ f ( x ) dx = F (b) − F (a)
a

b

INTEGRAL POR PARTES

∫ udv = uv − ∫ vduEXPONENTES

a n a m = a n+m an = a n− m am 1 a−n = n a 0 a = 1, si a ≠ 0

2

(a)m = m (a)
log b a =

n

n

LOGARITMOS

u = sen −1   + c a a −u du 2 2 ∫ u 2 ± a 2 = ln u + u ± a + c du 1−1 u ∫ u 2 + a 2 = a tan a + c du 1 u−a  ∫ u 2 − a 2 = 2a ln  u + a  + c  du 1  a+u   ∫ a 2 − u 2 = 2a ln  a − u  + c  u 2 2 a2 u a 2 − u 2 du = a − u + arcsen + c ∫ 2 2 a 2 u 2 a 2 2 2...
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