Fórmula cuadrática
Si a x 2 + b x + c = 0 , a x 2 + b x + c = 0 , x = – b ± b 2 – 4 a c 2 a x = – b ± b 2 – 4 a c 2 a
Triángulo de base b b h h
Área = 1 2 b h = 1 2 b h
Círculo de radio r r
Circunferencia = 2 π r = 2 π r
Área = π r 2 = π r 2
Esfera de radio r r
Superficie = 4 π r 2 = 4 π r 2
Volumen = 4 3 π r 3 = 4 3 π r 3
Cilindro de radio r r h h
Superficie curva = 2 π r h = 2 π r h
Volumen = π r 2 h = π r 2 h
Tabla
E1
Geometría
Trigonometría
Identidades trigonométricas
sen θ = 1 / csc θ sen θ = 1 / csc θ cos θ = 1 / sec θ cos θ = 1 / sec θ tan θ = 1 / cot θ tan θ = 1 / cot θ sen ( 90 0 – θ ) = cos θ sen ( 90 0 – θ ) = cos θ cos ( 90 0 – θ ) = sen θ cos ( 90 0 – θ ) = sen θ tan ( 90 0 – θ ) = cot θ tan ( 90 0 – θ ) = cot θ sen 2 θ + cos 2 θ = 1 sen 2 θ + cos 2 θ = 1 sec 2 θ – tan 2 θ = 1 sec 2 θ – tan 2 θ = 1 tan θ = sen θ / cos θ tan θ = sen θ / cos θ sen ( α ± β ) = sen α cos β ± cos α sen β sen ( α ± β ) = sen α cos β ± cos α sen β cos ( α ± β ) = cos α cos β ∓ sen α sen β cos ( α ± β ) = cos α cos β ∓ sen α sen β tan ( α ± β ) = tan α ± tan β 1 ∓ tan α tan β tan ( α ± β ) = tan α ± tan β 1 ∓ tan α tan β sen 2 θ = 2 sen θ cos θ sen 2 θ = 2 sen θ cos θ cos 2 θ = cos 2 θ – sen 2 θ = 2 cos 2 θ – 1 = 1 – 2 sen 2 θ cos 2 θ = cos 2 θ – sen 2 θ = 2 cos 2 θ – 1 = 1 – 2 sen 2 θ sen α + sen β = 2 sen 1 2 ( α + β ) cos 1 2 ( α – β ) sen α + sen β = 2 sen 1 2 ( α + β ) cos 1 2 ( α – β ) cos α + cos β = 2 cos 1 2 ( α + β ) cos 1 2 ( α – β ) cos α + cos β = 2 cos 1 2 ( α + β ) cos 1 2 ( α – β )
Triángulos
Ley de los senos: a sen α = b sen β = c sen γ a sen α = b sen β = c sen γ
Ley de los cosenos: c 2 = a 2 + b 2 – 2 a b cos γ c 2 = a 2 + b 2 – 2 a b cos γ
Teorema de Pitágoras: a 2 + b 2 = c 2 a 2 + b 2 = c 2
Ampliaciones de la serie
Teorema del binomio ( a + b ) n = a n + n a n – 1 b + n ( n – 1 ) a n – 2 b 2 2 ! + n ( n – 1 ) ( n – 2 ) a n – 3 b 3 3 ! + ··· ( a + b ) n = a n + n a n – 1 b + n ( n – 1 ) a n – 2 b 2 2 ! + n ( n – 1 ) ( n – 2 ) a n – 3 b 3 3 ! + ···
( 1 ± x ) n = 1 ± n x 1 ! + n ( n – 1 ) x 2 2 ! ± ··· ( x 2 < 1 ) ( 1 ± x ) n = 1 ± n x 1 ! + n ( n – 1 ) x 2 2 ! ± ··· ( x 2 < 1 ) ( 1 ± x ) – n = 1 ∓ n x 1 ! + n ( n + 1 ) x 2 2 ! ∓ ··· ( x 2 < 1 ) ( 1 ± x ) – n = 1 ∓ n x 1 ! + n ( n + 1 ) x 2 2 ! ∓ ··· ( x 2 < 1 ) sen x = x – x 3 3 ! + x 5 5 ! – ··· sen x = x – x 3 3 ! + x 5 5 ! – ··· cos x = 1 – x 2 2 ! + x 4 4 ! – ··· cos x = 1 – x 2 2 ! + x 4 4 ! – ··· tan x = x + x 3 3 + 2 x 5 15 + ··· tan x = x + x 3 3 + 2 x 5 15 + ··· e x = 1 + x + x 2 2 ! + ··· e x = 1 + x + x 2 2 ! + ··· ln ( 1 + x ) = x – 1 2 x 2 + 1 3 x 3 – ··· ( | x | < 1 ) ln ( 1 + x ) = x – 1 2 x 2 + 1 3 x 3 – ··· ( | x | < 1 )
Derivadas
d d x [ a f ( x ) ] = a d d x f ( x ) d d x [ a f ( x ) ] = a d d x f ( x ) d d x [ f ( x ) + g ( x ) ] = d d x f ( x ) + d d x g ( x ) d d x [ f ( x ) + g ( x ) ] = d d x f ( x ) + d d x g ( x ) d d x [ f ( x ) g ( x ) ] = f ( x ) d d x g ( x ) + g ( x ) d d x f ( x ) d d x [ f ( x ) g ( x ) ] = f ( x ) d d x g ( x ) + g ( x ) d d x f ( x ) d d x f ( u ) = [ d d u f ( u ) ] d u d x d d x f ( u ) = [ d d u f ( u ) ] d u d x d d x x m = m x m – 1 d d x x m = m x m – 1 d d x sen x = cos x d d x sen x = cos x d d x cos x = – sen x d d x cos x = – sen x d d x tan x = sec 2 x d d x tan x = sec 2 x d d x cot x = – csc 2 x d d x cot x = – csc 2 x d d x sec x = tan x sec x d d x sec x = tan x sec x d d x csc x = – cot x csc x d d x csc x = – cot x csc x d d x e x = e x d d x e x = e x d d x ln x = 1 x d d x ln x = 1 x d d x sen −1 x = 1 1 – x 2 d d x sen −1 x = 1 1 – x 2 d d x cos −1 x = – 1 1 – x 2 d d x cos −1 x = – 1 1 – x 2 d d x tan −1 x = 1 1 + x 2 d d x tan −1 x = 1 1 + x 2 Integrales
∫ a f ( x ) d x = a ∫ f ( x ) d x ∫ a f ( x ) d x = a ∫ f ( x ) d x ∫ [ f ( x ) + g ( x ) ] d x = ∫ f ( x ) d x + ∫ g ( x ) d x ∫ [ f ( x ) + g ( x ) ] d x = ∫ f ( x ) d x + ∫ g ( x ) d x ∫ x m d x = x m + 1 m + 1 ( m ≠ – 1 ) = ln x ( m = −1 ) ∫ x m d x = x m + 1 m + 1 ( m ≠ – 1 ) = ln x ( m = −1 ) ∫ sen x d x = – cos x ∫ sen x d x = – cos x ∫ cos x d x = sen x ∫ cos x d x = sen x ∫ tan x d x = ln | sec x | ∫ tan x d x = ln | sec x | ∫ sen 2 a x d x = x 2 – sen 2 a x 4 a ∫ sen 2 a x d x = x 2 – sen 2 a x 4 a ∫ cos 2 a x d x = x 2 + sen 2 a x 4 a ∫ cos 2 a x d x = x 2 + sen 2 a x 4 a ∫ sen a x cos a x d x = – cos 2 a x 4 a ∫ sen a x cos a x d x = – cos 2 a x 4 a ∫ e a x d x = 1 a e a x ∫ e a x d x = 1 a e a x ∫ x e a x d x = e a x a 2 ( a x – 1 ) ∫ x e a x d x = e a x a 2 ( a x – 1 ) ∫ ln a x d x = x ln a x – x ∫ ln a x d x = x ln a x – x ∫ d x a 2 + x 2 = 1 a tan −1 x a ∫ d x a 2 + x 2 = 1 a tan −1 x a ∫ d x a 2 – x 2 = 1 2 a ln | x + a x – a | ∫ d x a 2 – x 2 = 1 2 a ln | x + a x – a | ∫ d x a 2 + x 2 = senh −1 x a ∫ d x a 2 + x 2 = senh −1 x a ∫ d x a 2 – x 2 = sen −1 x a ∫ d x a 2 – x 2 = sen −1 x a ∫ a 2 + x 2 d x = x 2 a 2 + x 2 + a 2 2 senh −1 x a ∫ a 2 + x 2 d x = x 2 a 2 + x 2 + a 2 2 senh −1 x a ∫ a 2 – x 2 d x = x 2 a 2 – x 2 + a 2 2 sen −1 x a ∫ a 2 – x 2 d x = x 2 a 2 – x 2 + a 2 2 sen −1 x a
